Advancements In triaxial Testing

ADVANCEMENTS IN TRIAXIAL TESTING
DEVELOPMENT OF A CANTILEVER-TYPE LOCAL DEFORMATION TRANSDUCER FOR MEASURING AXIAL RADIAL STRAINS IN TRIAXIAL TESTS 

1.Introduction

Triaxial testing is one of the most popular and versatile apparatus for laboratory characterization of specimens which is globally acceptable. The conventional triaxial system takes measurement of a specimen through transducers located outside the triaxial cell. This paper presents of advanced triaxial testing options that are available to determine samples of properties typically unobtainable with conventional old triaxial systems, or sample response that is more closely representative any conditions. The use of a local strain measurement device in triaxial test is becoming standard practice due to the awareness that the knowledge of nonlinear stress-strain behaviour of samples at small and intermediate strain levels is necessary for accurate deformation analysis of geotechnical structures. During the past two decades, different local strain measurement systems have been developed by various institutions. As far as local axial strain is concerned, there are: (ii) Hall effect local strain gages (e.g., Clayton and Khatrush 1986), (iii) prox- imity transducers (e.g., Hird and Yung 1989), (iv) original-local deformation transducers (original-LDT) (e.g., Go to et al. 1991), and (v) LVDTs (e.g., Cuccovillo and Coop 1997).
Because the costs of these systems are very high and the manufacture of them is expensive. The least expensive option is to develop an in-house made LDT tester, which uses pressure gauges. The cantilever-type local distortion transformer (cantilever-LDT) was developed in this study as an alternative axial voltammeter.
The review classifies the local small strain measuring instrumentation based on the technology applied and the ability of the same system to measure both axial and radial strain. Based on the technology applied, the instruments are classified in this paper, which are electrical and fibre optic base respectively. These gauges are also classified based on ability of a single type of transducer to obtain axial and radial strain measurement were show in figure.

2. Background

There are many research papers published on linear deformation transducer (LDTs) and many experimental techniques are used as follows:
2.1. Linear deformation transducer (LDT)
LDT is a system consisting four strain gauges, two thin flexible strip of phosphor bronze and four pseudo-hinged fabricated to form local deformation transducers (LDTs). Two strain gauges are attached to the centre of each strip which is mounted in between a couple of pseudo-hinged adhered to the triaxial membrane using powerful glue and the whole setup aligned vertically. During the test, the deformation of the specimen causes the distance between the two attachments to change. The changes are then detected by the strain gauges and recorded as an axial strain. The average of readings obtained from the strain gauges is taken as an axial strain. The instrument can measure strain as low as 0.001%. Nonlinear calibration, errors due to noise from the amplifier, hysteresis of LDTs, mechanical imperfections and variation of voltage inputs couple with shallow working range have crippled the performance of this transducer. In addition, the contact force between the membrane and the hinges tend to increase with increase in deformation which leads to error. The setup of LDTs on the triaxial specimen is shown in Fig. 8. This device has been utilized by Goto et al. (1991) and Tatsuoka (1992).

 Fig. 1 : Schematic view of LDTs on triaxial (Goto et al, 1991)

2.2. Linear differential variable transducer (Lvdt)

LVDT is one of the most popular and old device for measuring stiffness at small strain. It was first developed by Brown and Snaith (1974). Nowadays it has obtained commercial values in the sense that even industries employ LVDT for soil strain analysis. Basically, there are two types of local LVDTs according to the nature of support; the floating type and the fixed type. The earlier floating type LVDT (Brown and Snaith, 1974) was supported by two circular split-sprung collars which are circumferentially mounted on the targets embedded in to the soil specimen at both ends of the gauge length (Fig. 2a). The setup allows the respective movement of the targets to be recorded by two LVDTs attached diametrically opposite to each other. However, the LVDT is big and its entire weight is supported by the soil which can cause failure apart from inability of the LVDT to work inside water. Costa Filho (1985) developed a fixed support type, whereby the LVDTs are mounted on a fixed support (Fig. 2b) which reduces the impact of the weight of LVDTs on the specimen. The fixed type of support causes jamming of the LVDT especially near failure of the specimen and the LVDTs are also nonsubmersible in water. Cuccovillo and Coop (1997) developed a small size, water submersible, easy to mount and align LVDTs (Fig. 2c) which has made remarkable improvement over the previously used LVDTs that were big and insensitive over certain linear distance. The previously developed nonsubmersible LVDT had many disadvantages and the focus of our subsequent discussion will be on the submersible LVDT as it is currently the type adopted for local strain measurement. Cuccovillo and Coop (1997) also developed radial strain LVDTs which allows measurement of both radial and axial strain using the same type of device simultaneously. LVDT was employed by Gasparre et al. (2007) in determining the stiffness of natural London clay. Another research conducted with LVDTs include.
However, it is costly and susceptible to jamming towards failure because of core tilting. Apart from that, it also requires great care during setting up of both the apparatus and the sample to ensure uniform and concentric loaded specimen for the instruments to perform accurately

Fig.2, Diagrammatic representation of LVDT; (a) Floating type LVDT (Brown and Snaith, 1974); (b) Fixed support type (Costa Filho, 1985); (c) Water submersible LVDT (Cuccovillo and Coop, 1997)

2.3. hall effect transducer

The working principle of Hall Effect transducers is based on the fact that when a semiconductor plate is exposed to a magnetic field such that the flux lines are oriented perpendicular to the plate and flow of current, electromotive force (EMF) is produced across the plate normal to the flowing current. The instrument consists of two parts; the upper pad which is fixed on the specimen holding a suspended pendulum mounted on a spring that clutch the magnetic assembly. The lower part comprises of a metallic container which hold the semiconductor. This part is also fixed on the specimen. The Hall Effect transducer resolution is ˂0.1µm, and the accuracy is up to ±0.2% full range output (FRO) over 4mm range. Over 5 mm range, the accuracy is ±0.3% FRO while over 6 mm range is ±0.4% FRO. The device is suitable for variety of sample size ranging from 38 mm – 150 mm including customized specimens. The semiconductor chip most be compensated against temperature and changes in the DC voltage supply. Studies conducted with Hall Effect transducer includes: Clayton et al. (1989), Difficulties in alignment of Hall Effect transducers on a triaxial soil specimen, rotation of lower pad in some cases while conducting triaxial test, are the limitations of Hall Effect transducer. Fig. 4 describes Tatsuoka et al. (1990), Ng and Wang (2001), Ng et al. (2009), Clayton (2011), Muñoz-Castelblanco et al. (2012), and Wu et al. (2014) the schematic view of Hall Effect transducers on a soil sample.

Fig.3: Diagram of hall effect transducers on a triaxial specimen
(Clayton and Khatrush, 1987)

2.4. theory of axial and radial strains

The regional axial strain of a triaxial test sample can be determined by placing two displacement transmitters all over the middle portion of the sample, aligned vertically as well as 180° away. Figure 4 shows the Hall Effect displacing transmitters in action, but other transducer kinds, such as the tiny Linear Variable Differential Transformer (LVDT), might also be used. Two fixed pieces secure each transducer to both the specimens, which lie close to each other and to the sample deformations. As a result of the transducers tracking this movement, the regional axial strain measurements must be calculated using a test specimen (the distance between mounting blocks) rather than the initial large impression.

Fig.4a: Schematic illustration of the axial and lateral LDT setup in the triaxial test

The localised axial strain is measured at opposite wings of both the specimen using 2 sets of cantilever LDTs in symmetrically opposing directions, and the average is utilised for analytics Stationary.
The local axial strain can then be calculated using the relative movements of these two sites (see Fig. 4b) The cantilever-production LDT’s process is based on the same principles as the original-LDT introduced by Hoque et al (1997).

Radial Strain
One of the main intentions with the system developed was to measure radial strains directly rather than by way of a radial belt mechanism. In the system described here, measurements are made at three independent positions and so a better average radial strain determination is achieved compared with what is in fact a relative change across a single diameter as obtained with a radial belt. Equally it is not possible to detect any lateral sample translation with a radial belt because it operates in a floating mode (although in most cases this is negligible). Another disadvantage of most radial belt systems is that the diameter change is usually measured indirectly by way of a hinged mechanism. With the system described here, as the devices are fixed and independent of the sample, they can be positioned quickly with minimal interference when setting up the sample
Adopting LVDTs is a logical choice as they have been used extensively and found to have excellent resolution, accuracy, repeatability and robustness (e.g. Cuccovillo & Coop, 1997). One approach would be to set up the LVDT devices horizontally and perpendicular to the radial boundary, in a fixed mode, with the armature bearing directly onto the sample boundary. Such a system was used by Kok (2006) with three LVDTs spaced at 120° and passing through a specially made ‘access ring’ to accommodate them, as shown in Fig. 5 (this system was designed and manufactured by the first author)

Fig.5. Details of the Radial measuring system used by kok (2006) : a plan view ; (b) Section through access ring and one of the radial LVDTs

Frequently with radial strain systems the measurements are made across a diameter, which would not detect any bending or distortion in the perpendicular plane. This is equally true for axial strain measurements involving two devices diametrically mounted on opposite sides of the sample. Using three LVDTs spaced radially at 120° provides a more reliable measure of average strain across the section of the sample where the measurements are made.
The key element of the system is the L-shaped component. It pivots about a stainless steel pin of 1•57 mm (1/16 in) diameter, which sits within a hole of essentially the same diameter: there is negligible play and during its operation its weight holds it firmly in position (it does have a minimal sideways play to allow free rotation). Its mechanism and how radial displacements are translated to vertical movements of the LVDT armature are shown schematically in Fig. 4. A detailed outline of the relevant components and key contact points is shown in Fig. 6(a) with the LVDT armature orientated vertically and screw horizontally in an idealised initial position. The main focus is on the contact point A.
In Fig. 6(b) the solid lines represent the distances between the axis of the pivot point O (the ‘origin’) and the respective contact points A and B; broken lines are drawn along the axes of screw and LVDT armature and perpendiculars from them to the pivot origin O. An increase in radius of the sample results in A following a circular arc trajectory to A′ with distances OA and OA′ being equal. The contact point A has moved from the mid-position on the surface of the rounded head to the point A′ slightly above it. At the other end of component, the radial expansion is translated as an upwards movement of the LVDT armature, which, being within the body of the LVDT, is constrained to stay in the same horizontal position. As with the screw, the contact point B is initially at the mid-point of the rounded base but as the armature moves up the contactpoint B′ shifts to the left of this point. Distance OB′ is greater than OB and increases with continuing radial expansion.
In view of the complex changing geometry and the uncertainty of the rounded heads of screw and the lower end of the LVDT armature being perfectly spherical, it is not realistic to rely on a geometrically determined relationship between displacements of the LVDT armature with those of the radial boundary of the sample.

Fig.6. schematic diagram of rotating mechanism : (a) primary Component; (b) geometry illustrating Modes of Rotation and Relative arc length to key contact points .

2.5. other local radial strain measuring techniques

Small strain measuring devices have been discussed in the previous sections. However, it is worth to mention other techniques of measuring local radial deformation. Lateral strain device with resolution of 0.04% was illustrated by El-Ruwayih (1976). Boyce and Brown (1976) illuminated that local radial strain can be measured using radial strain ring with resolution of 0.0005%. The use of lateral strain collar with resolution of 0.01% was demonstrated by Kolymbas and Wu (1989). Another technique of using resistance wire transducer was illustrated by Skopek and Cyre (1995). Comparatively, there is no much data regarding the accuracy of these devices in the literature.

2.6. Types of tests

2.6.1.unconfined Compression test

The unconfined compression test is by far the most popular method of soil shear testing because it is one of the fastest and cheapest methods of measuring shear strength. The method is used primarily for saturated, cohesive soils recovered from thin-walled sampling tubes. The unconfined compression test is inappropriate for dry sands or crumbly clays because the materials would fall apart without some land of lateral confinement. To perform an unconfined compression test, the sample is extruded from the sampling tube. A cylindrical sample of soil is trimmed such that the ends are reasonably smooth and the length-to-diameter ratio is on the order of two. The soil sample is placed in a loading frame on a metal plate; by turning a crank, the operator raises the level of the bottom plate. The top of the soil sample is restrained by the top plate, which is attached to a calibrated proving ring. As the bottom plate is raised, an axial load is applied to the sample. The operator turns the crank at a specified rate so that there is constant strain rate. The load is gradually increased to shear the sample, and readings are taken periodically of the force applied to the sample and the resulting deformation. The loading is continued until the soil develops an obvious shearing plane or the deformations become excessive. The measured data are used to determine the strength of the soil specimen and the stress-strain characteristics. Finally, the sample is oven dried to determine its water content. The maximum load per unit area is defined as the unconfined compressive strength, qu. In the unconfined compression test, we assume that no pore water is lost from the sample during set-up or during the shearing process. A saturated sample will thus remain saturated during the test with no change in the sample volume, water content, or void ratio. More significantly, the sample is held together by an effective confining stress that results from negative pore water pressures (generated by menisci forming between particles on the sample surface). Pore pressures are not measured in an unconfined compression test; consequently, the effective stress is unknown. Hence, the undrained shear strength measured in an unconfined test is expressed in terms of the total stress.

2.6.2. Triaxial test

This includes why the test is performed and how it is performed. The paper will look at systems for triaxial tests, the stages of a triaxial test, some of the theory behind triaxial tests and also automation of the test process.

There are three primary triaxial tests conducted in the laboratory, each allowing the soil response for differing engineering applications to be observed. These are:
• Unconsolidated Undrained test (UU)
• Consolidated Undrained test (CU)
• Consolidated Drained test (CD)

A typical triaxial test involves confining a cylindrical soil or rock specimen in a pressurised cell to simulate a stress condition and then shearing to failure, in order to determine the shear strength properties of the sample. Most triaxial tests are performed on high quality undisturbed specimens. The samples normally range from 38 mm to 100 mm samples, although samples considerably larger can be tested with the correct equipment. The test specimen most commonly has a height to diameter ratio of 2:1.
The sample will usually be saturated, then consolidated and finally sheared, most commonly only in compression – but extension tests may be undertaken with the correct equipment.
The main difference between Unconfined compression test and triaxial compression test is that in this test the confining cell pressure is kept zero during the test, in fact it is a special case of triaxial test. Due to which without applying any lateral pressure like a concrete crushing test the cylindrical soil sample is crushed to failure. Although this test can also be done by using triaxil test in the laboratory but instead we move towards a simpler portable piece of equipment which is known as unconfined compression test apparatus. Due to its portable design the equipment can easily be shifted to the desired site and the test can be done within the field.

3. Aim and Objectives

The aim of this Master thesis is the development of a cheap yet robust system for measuring axial and radial strains in triaxial tests.
To do this, we will develop a cheaper and less expensive type of cantilever for measuring soil deformation in the triaxial test. It can give new measurement approach, new analysis and techniques for small deformations of soil, Clay and rock specimen. The sample preparation as well as setup are critical for obtaining valid local axial strain data sets. They feature a high magnification, high efficiency, multiplexing, multifunctionality, and are lightweight.

4. Methodology

A modified traditional triaxial system was used to install the LDT. The schematic setup of the test apparatus is shown in below figure. The LDT was calibrated and then fixed on the surface of the soil specimen by two hinges. As mentioned early, an initial bending should be applied so that the distance between the two hinges was kept shorter than the length of the LDT. It should be noted that the initial bending depends on the cyclic test settings, because the LDT will experience both extension and compression during cyclic tests. Two LDTs were mounted on the surface of the specimen in diametrically opposite to each other. The test system includes a triaxial test chamber with a loading frame, pressure supply devices, the LDT, fiber optic sensing interrogator and computer. The LDT was used to measure the local deformation with the maximum strain. Four different tests were conducted with different confining pressure.
The cantilever-type local deformation transducer (cantilever- LDT) was developed in this study as an alternative local axial strain measurement device. In this paper, its manufacturing process, setup, and calibration procedure are described. Some triaxial test results will take on stiff Clay, soft clay, and rock specimens are presented to evaluate the performance of the cantilever-LDT. Its advantages and limitations are discussed by comparing with the performance of the original-LDT by Goto et al. (1991).
We will work on the arrangement of axial and radial strain to give the accurate results and also we are follow the the design from the previous research paper
In order to measure the vertical movement of two points on specimen surface, two cantilever-LDTs are placed along the same vertical alignment but at different levels as shown in Fig. 8. The relative movement of these two points can then be used to derive the local axial strain. Two pairs of cantilever LDTs at a diametrically opposite direction are used to measure the local axial strain at two sides of the specimen and the average is used for data analysis. Our research is on the soft soil , stiff clay, and rocks in our testing plans. These specimens we are using in our system in tri-axial test.
We will develop a system of compact design which will give accurate results, with lesser time consumption of a good Quality and at the same time reliable in cheaper costs. For Making all of this we need to make some adjustment in the measurements of the original system.
Two cantilever-LDTs are placed on the same vertical align- ment but at different levels of a specimen to measure the vertical movement of two points on the specimen surface as shown in Fig.
Many of the existing local axial transducers can be configured to measure local radial strain. Therefore, it is possible to measure both axial and radial strain from the same type of device. Several types of local radial strain transducers exist and most of them have no reported studies regarding their accuracy (Yimsiri and Soga, 2002). We will work on the accuracy and reliable results carried out by the triaxial system.
It can provide novel measuring methods, analyses, and procedures for minor deformations in soil, clay, including rock specimens, as well as work mostly on the system’s structure to make it more efficient and feasible through some new advancement.
The cantilever-LDT was made with a thermally phosphor bronze strip. The strips were around 25 mm long (excluding the cantilever part), 5 mm broad, but 0.35 mm thick. To build a full Wheatstone Bridge circuit with optimal sensibility and temperature adjustment, four etched aluminium strain gauges (two on one side as well as two on the other) were placed towards the fixed end of the strip.
Two cantilever-LDTs are mounted more along the vertical orientation but at multiple stages to evaluate the vertical motion of two spots on the sample surface, as shown in Fig. The regional axial strain could then be calculated using the lateral motion of these two sites.

L – HINGE:-A tiny cylindrical cylinder (1.0 mm diameter but also 5 mm long) was mounted to the open edge of the cantilever-LDT to provide a metal ring for an experiment, as illustrated in Fig. 1. The tube was fastened to a soil sample through an L-hinge (8 mm long for every arm and 1.2 mm thick with a pin 7 mm long and 0.6 mm diameter). The L-hinge was pressed via the rubber membrane but instead superglued to the rubber membrane.
Wires: -The cantilever-LDT was coupled to a transducer box for induction generator, output amplifying, and filtering after passing through the outflow at the bottom of a triaxial tank. 3-V dc was used to power the bridge circuit.
The signal-to-noise ratio was lowered as a result of both the stacking procedure, which boosted the recorded digital signal resolution. The data capture rate was around 11 000 samples/s, resulting in a total time of about 1 second for each readout of all stations (ten in this example). For a repeated load test, this time span was thought to be unimportant. As shown in Fig. 1, two cantilever-LDTs are mounted along such vertical alignment at various stages to evaluate the directional motion of two spots on the sample’s surface.
Another of the characteristics of the cantilever-LDT and over original-LDT would be its capacity to discharge itself under significant strains.

To measure the relative motion of two places on the sample surface, two cantilever-LDTs are mounted along the same vertical orientation but at separate levels of both the sample, as shown in Fig.
Figure 7 shows a diagram of both the cantilever-LDT. 8 It uses the same instrument method as the initial LDT (Goto et al. 1991), with the exception that it uses a cantilever beam.

The system we want to implement in Master thesis is based on the previous work done by Yimsiri and Soga (2002).

4.1. Measurement of Axial Strain

The localised axial strain is measured at opposite wings of both the specimen using 2 sets of cantilever LDTs in symmetrically opposing directions(each set contains 2(see Fig. 9)(, and the average is utilised for analytics Stationary.
The relative movements of these two points can then be used to derive the local axial strain (see Fig. 9). The manufacturing process of the cantilever-LDT is similar in principle to that of the original LDT presented by Hoque et al. (1997).

Fig9: a schematic Diagram of Axial Strain

Fig.10.configuration during compression shearing

The free end of the cantilever-LDT was attached with a small cylindrical tube (1.0-mm diameter and 5 mm long) to provide a contact point to a specimen as shown in Fig. 9. The tube was placed against a L-hinge (8 mm long for each arm and 1.2 mm thick with a pin 7 mm long and 0.6 mm diameter), which was attached to a soil specimen. The L-hinge was pinned through the rubber membrane and also glued on to the rubber membrane by Superglue.
In addition, the theoretical analysis could help to design the LDT for various applications, such as adjusting the measurement accuracy and range though the parameter for different conditions. It can also be obtain from the theoretical analysis that the sensitivity of the axial deformation Δ measured by the LDT can be increased by a larger thickness and shorter length of the LDT. From the assumptions of the theory, we can also understand that the LDT is limited to small deformation measurements as it was assumed to be deformed as a first model of bulking. However, the measurement range of deformation can be increased with larger length and a thin LDT material The average of each 1000 data was used for data analysis. This stacking process reduced the signal-noise ratio and, hence, increased the resolution of recorded signal. The data acquisition rate was approximately 11 000 samples/s, which made the total time required for each reading of all channels (ten in this case) approximately 1 s. It was considered that this time interval was not critical for a static loading test.

4.2. Measurement of Radial Strain

Fig 11: schematic Diagram Of Radial Strain

For the Radial strain stage, we will rotate it 90°.

The importance of local radial strain measurements will never be overemphasized. In movement of the fibre and the specimen. Deformation data is acquired at every increment from local LVDTs and the fibre optic sensor. The results showed strong similarities between the Young’s modulus measured from both instruments. Measurement of both circumferential and axial strains was obtained from the fibre sensing technique while LVDT gave only the partial view of the deformation.

order obtain bulk modulus and poison’s ratio, it is necessary to determine radial strain. Many of the existing local axial transducers can be configured to measure local radial strain. Therefore, it is possible to measure both axial and radial strain from the same type of device. Several types of local radial strain transducers exist and most of them have no reported studies regarding their accuracy (Yimsiri and Soga, 2002). The classification of the transducers based on their ability to measure radial and axial strain was given in Fig. 11. Local radial LVDTs that uses mercury indicator column with resolution of 0.025% was invented by Bishop and Henkel (1957). Floating-type lateral strain LVDT suitable for use in air and transformer oil was discussed by Yuen et al. (1978). Radial proximity transducer was introduced by Hird and Yung (1989) and Shibuya et al. (1994). It was then adopted by Yimsiri and Soga (2011) and Yimsiri and Soga (2002). The technology behind the transducers, the principle of operation, advantages and disadvantages of each technique including how they a mounted on the specimen were discussed This paper also discussed the trend of advancement of LDT and the transformation of the technology from electrical to fiber optics. Conjecture helical configuration from distributed fiber optics technology was examined. The selection of these instruments by the user is based on the application, requirements, availability and cost. It can be highlighted that development of local radial strain measuring instrumentation is still limited, which brings the need for more studies in this part.
Many other robust techniques that show potentials for use in measuring stiffness at small strain accurately are yet to be implemented. For instance, FBG sensing technology can be employed directly for determining deformation characteristic of materials in the laboratory. FBGs are used as strain sensors, temperature sensors pressure sensors, and for measuring flow rate because they have high resolution, high accuracy, high precision, multiplexing, multifunctional and are light in weight. They also have good resistance to lightning, electromagnetic interference, and electrical short circuiting.

4.3. PERFORMANCE OF cantilever type system (ldt)

In this thesis we are using the four types of specimens were as soft clay, stiff clay, compacted soil and clay rock. These specimens are used in the triaxial test. There are10 Unconfined compressive strength (UCS)tests and 4 triaxial test. The reference between these two is the Unconfined compressive strength (UCS),we will put the sample in the load frame without any triaxial chamber just axial compression without fluid and cell pressure. But in 4 triaxial test we will use triaxial cell. And we will check the accuracy of the triaxial test of cantilever LDT.
Soft clay : Softclay is defined as soils with large fractions of fine particles such as silty and clayey soils, which have high moisture content, peat foundations and loose sand deposits, located near or under the water table (Kamon and Bergado, 1991).
Stiff clay: The stiffness of a clay is largely an index of its moisture content. The current definition of ‘stiff’ relates strictly to consistency.
Compacted Soil: soil compaction is the process in which stress applied to a soil causes densification as air is displaced from the pores between the soil grains.
Clayrock:Clay is a type of fine-grained natural soil material containing clay minerals. Clays develop. Shale, formed largely from clay, is the most common sedimentary rock.

5. Research plan

We will obtain the valuation of axial strain, radial strain and volumetric strain during compression, consolidation and shearing for 4 materials we will use. From triaxial test and compression test. the observation of the test will be carried with the minimal accuracy so that we can match the previous researchers. To evaluate, a minimal accuracy of 4 percent -10 percent is required for soft soil to evaluate to accomplish that stiff clay but also rock is to have a minimum measurement precision of 0.0012 to 0.003 and a working range of 6%

6. REFERENCE

Ackerley SK, Standing JR, and Hosseini Kamal R (2016). A system for measuring local radial strains in triaxial apparatus. Géotechnique, 66(6): 515-522.
Baldi, G., Hight, D. W., and Thomas, G. E., 1988, “A Revaluation Reference of Conventional Triaxial Test Methods.” Advanced Triaxial Test ing of Soil and Rock, ASTM STP 977, T. Donaghe, R. C. Chaney, and M. L. Silver, Eds., ASTM International, West Conshohocken,
Boyce JR and Brown SF (1976). Measurement of elastic strain in granular material. Geotechnique, 26(4): 637-640
Clayton CR, Khatrush SA, Bica AVD, and Siddique A (1989). The use of Hall effect semiconductors in geotechnical instrumentation. Geotechnical Testing Journal, 12(1): 69-76.
Clayton CRI (2011). Stiffness at small strain: research and practice. Géotechnique, 61(1): 5-37.
Cuccovillo T and Coop MR (1997). The measurement of local axial strains in triaxial tests using LVDTs. Géotechnique, 47(1): 167-171.
Enomoto T, Koseki J, Tatsuoka F, and Sato T (2016). Rate dependent behaviour of undisturbed gravelly soil. Soils and Foundations, 56(3): 547-558.
Gasparre A, Nishimura S, Minh NA, Coop MR, and Jardine RJ (2007). The stiffness of natural London Clay. Géotechnique, 57(1): 33-47.
George Rodriguez, Joseba Zubia,,2017,”a new measurement Approach for small deformation of soil specimens:
Goto, S., Tatsuoka, F, Shibuya, S., Kim, Y.- S., and Sato, T., 1991. “A Simple Gauge for Local Small Strain Measurements in the Laboratory,” Soils and Foundations, Vol. 31. No. 1. pp. 169-180.
Hird, C. C. and Yung, P. C. Y., 1989, “The use of proximity transducers for local strain measurements in triaxial tests,” Geotechnical testing journal, Vl. 20, No.2, pp. 149-167.
Hoque, E., Sato., T., and Tatsuoka, F., 1997, “Performance evaluation of LDT’s for using in Triaxial tests,” Geotechnical testing journal, Vol.34 No3, pp 323-340
Jardine, R.J., Symes, M.J., and Burland J.B., 1984, “The measurement of soil stiffness in the triaxial apparatus, “Geo technique, Vol 34, No 3, pp.323-340
Kolymbas D and Wu W (1989). A device for lateral strain measurement in triaxial tests with unsaturated specimens. Geotechnical Testing Journal, 12(3): 227-229.
Muñoz-Castelblanco, Delage P, Pereira JM, and Cui YJ (2012). Onsample water content measurement for a complete local monitoring in Triaxial testing of unsaturated soils. Géotechnique, 62(7): 595–604
Scholey, G. K., Frost, J. D., Lo Presti, D. C. F., and Jamiolkowski, M., 1995, “A Review of Instrumentation for Measuring Small Strains During Triaxial Testing of Soil Specimens.” Geotechnical Testing Journal, Vol. 18, No. 2, pp. 137-156.
Symes, M. J. and Burland, J. B., 1984, “Determination of Local Displacements on Soil Samples,” Geotechnical Testing Journal, Vol. 7. No. 2, pp. 49-59.
Uchida S, Levenberg E, and Klar A (2015). On-specimen strain measurement with fiber optic distributed sensing. Measurement, 60: 104-113.
Wu C, Ye G, Han L, and Wang J (2014). Preliminary study on smallstrain triaxial testing method for soft shanghai clays. In the Soil Behavior and Geomechanics, Shanghai, China: 379-388.

• Yimsiri S and Soga K (2011). Cross-anisotropic elastic parameters of two natural stiff clays. Geo technique, 61(9): 809-814.
  Yimsiri S, Ratananikom W, and Likitlersuang S (2009). Investigation of some anisotropic characteristics of Bangkok Clay. In the 17th International Conference on Soil Mechanics and Geotechnical Engineering, Alexandria, Egypt: 1068-1071.
  Yimsiri, S. and Soga, K., 2002, “A Review of Local Strain Measurement Systems for Triaxial Testing of Soils,” Geotechnical 7 Engineering, SEAGS, Vol. 33, No. I. pp. 41-52.