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Large-Scale Triaxial Apparatus .1 Calibration of the Applied Axial Stress



4.3.3 Large-Scale Triaxial Apparatus .1 Calibration of the Applied Axial Stress

By using a revolving bearing system, the loss of applied axial stress due to friction between the ram and chamber collar was minimized. This bearing system allowed the piston to fall gradually under its own weight. However, it was imperative to ensure that the axial stress applied on the top of specimen was the stress measured by the pressure transducer fitted to the cylinder of the axial loading unit. This process began with the

0 400 800 1200

Water pressure, (kPa)

0 20 40 60

Measured longitudinal strains, (microstrain)


Figure 51. Calibration of vertical strain gauges (left and right, top and bottom)

calibration of the digital display to read the pressure measured by the transducer (Shaevith) in kPa. To facilitate this, the pressure transducer was fitted to a Budenberg air dead weight tester and connected to the control board. The weight was applied and then removed in 10 kPa increments and checked against the digital display. This procedure was repeated three times to ensure consistency of the results. The accuracy of the transducer was found to be 0.035 %, corresponding to a small deviation of 1.4 kPa over the transducer full range of 4 MPa.

For the calibration of the applied axial stress, a stiff steel column 300 mm in diameter and 500 mm in height was placed inside the triaxial chamber on the bottom platen. An Interface load cell with maximum capacity of 445 kN (equivalent to 6.3 MPa over the steel column area) was then positioned on the top of the column. After connecting the

Chapter 4: Test equipment and calibration

load cell to a HMB strain meter calibrated to read the load in kN, the pressure transducer was connected to the digital display on the triaxial apparatus console/control board. No connections were made for the confining pressure for this calibration step. The axial stress was applied in increments at 15 minute intervals. The applied axial stress was plotted against the force measured by the load cell, converted to stress over the area of the column top, and is shown in Fig. 52. This relationship was applied for the correction of axial pressure monitored during triaxial tests. Calibration of Pressure Transducers

The Shaevith pressure transducers used to monitor both the confining pressure and pore water pressure were calibrated using a similar method and the same Budenberg air dead weight tester as for the hydraulic pressure transducer. However, the increment of applied pressure for both transducers was reduced to 2 kPa. Their accuracy was found to be 0.015 % for the transducer measuring the confining pressure, whilst the accuracy of the back pressure/pore water pressure transducer was 0.02 %. Initially, the calibration of pressure transducers was performed monthly. During later stage of testing program, the calibration was performed every three months, as the drift was not significant. Calibration of Volume Change

It was necessary to establish a correlation between the volume of water that flowed in and out of the triaxial cell and the upward or downward movement of piston inside the voluminometer cylinder. For this purpose, the voluminometer was disconnected from the cell and fitted to a vacuum device. While the top part of the cylinder was subjected to a vacuum, the bottom part was filled with de-aerated water supplied from the

0 400 800 1200

Applied axial stress, (kPa)

0 400 800 1200

Measured axial stre ss, (kPa)

σmeas = 1.00508 σappl -3.76503 (kPa)

Figure 52. Calibration of the axial loading unit

confining pressure tank. The connections were then exchanged so the bottom part of the voluminometer was connected to the vacuum device and the top part to the confining pressure tank. By repeating this procedure several times, air bubbles were eliminated from the inside the voluminometer cylinder and along the connecting plastic tube.

When the filling process was completed, water under pressure was supplied to either the top part or the bottom part of the cylinder causing the piston to move downward or upward. This movement was monitored using the Gefran LVDT fitted to the piston.

The water that flowed out of the voluminometer was collected in a graduated burette placed on a balance with a special lid to prevent the evaporation of water. From the collected data, relationships were established (Fig. 53) between the vertical displacement of the piston and the volume of water entering and exiting the triaxial chamber.

Chapter 4: Test equipment and calibration

0 20 40 60 80 100

LVDT display, (mm)

0 1000 2000 3000

Volume of water, (ml)

Voldm= 34.6361(LVDT) - 2.4146 x 10 -7 (ml)

Volum= 34.3219(LVDT) - 2.6645 x 10 -14 (ml)

Piston moving upward Piston moving downward

Figure 53. Calibration of the voluminometer measurement

Three preliminary tests were performed at various confining pressures viz., 8, 60 and 240 kPa. The volume change measured from the voluminometer was checked against the measurements done by the burette connected to the specimen vacuum/drainage lines.

Figure 54 presents the results measured by both methods and the developed relationship was used to correct the volume change measurements during the test program.

However, the error associated with the voluminometer measurements corresponded to only a 0.0003 volumetric strain. Membrane correction

a. Correction for Membrane Strength

An extensive literature review was presented by Salman (1994) on the effect of membrane strength and the various methods used to correct test results for the membrane effect. It was concluded that if the compressive pressure was sufficient to

-3000 -2000 -1000 0 1000 2000

Voluminometer measurements, (ml)

-3000 -2000 -1000 0 1000 2000

Burette measurements, (ml)

Volbur= 0.98623 ( Volvlm) - 4.21994 (ml)

σ3= 15 kPa σ3= 60 kPa σ3= 240 kPa

Figure 54. Correction of volume change measurements

hold the membrane firmly against the specimen (i.e. no buckling of membrane occurred), then the membrane was capable of resisting compression, and hence the compression shell theory proposed by Henkel and Gilbert (1962) could be applied.

Assuming that the specimen deformed as a right cylinder, then the axial stress supported by the membrane could be computed by the slightly modified equation given by Fukushima and Tatsuoka (1984):

d ε ) ε (2 t E 3

σam =−8 m am+ θm (4.1)

where, σam is the axial stress taken by the membrane, Em is the Young’s modulus of the rubber membrane, t is the average thickness of the membrane, εam and εθm are the mean axial and circumferential strains in the membrane which were assumed equal to the

Chapter 4: Test equipment and calibration

averaged axial and radial strains on the specimen, and d is the initial diameter of the specimen.

The radial stress developed in the membrane is given by the expression (Fukushima and Tatsuoka, 1984):

d ε ) (ε 2

t E 3

σrm =−8 m am+ θm (4.2)

In the derivation of Eqs. (4.1) and (4.2), it was assumed that the Poisson’s ratio for the rubber was 0.5. Eqs. (4.1) and (4.2), or similar ones with slight modifications, had been used by several researchers (Duncan and Seed, 1967; Ponce and Bell, 1971; Molenkamp and Luger, 1981).

Fukushima and Tatsuoka (1984) also showed that at very low confining pressures, the hoop tension theory proposed by Henkel and Gilbert (1952) should be used. It was assumed that the low level of confining pressure did not resist the buckling effect of the neoprene membrane when subjected to axial compression, as schematically presented in Figure 55, a phenomenon which occurred over the whole area of the membrane.

Consequently, the resistance of the rubber membrane against axial deformation could be neglected. The equations presented by Fukushima and Tatsuoka (1984) are a modified version of those initially proposed by Henkel and Gilbert (1952), as given by:

d t E 2 0

m m rm




and σ ,




Figure 55. Schematic diagram of buckling of membrane (after Fukushima and Tatsuoka, 1984)

DeGroff et al. (1988) presented an alternative expression for estimating the radial stress developed in the rubber membrane which reduces the confining pressure:

( )

d ε E 4

σrm 3 m a

5 . 0

= (4.4)

where εa is the axial strain and the other parameters are those defined previously.

More recently Kuerbis and Vaid (1990) showed that, by considering the variation in the membrane thickness due to extension, Young’s modulus for rubber could be kept constant in the expression of axial and radial stresses developed within the neoprene membrane. The modulus of the rubber could be measured using the same method proposed by Henkel and Gilbert (1952), but the calculations should take into account the change in the cross-sectional area of the rubber membrane. This method also considered that the axial and radial stains were interdependent, where a change of one induced a variation of the other due to the Poisson’s ratio of the material. The

Chapter 4: Test equipment and calibration

expressions of the axial and radial stress in the rubber membrane are given by:

ε ) ε (2 d

)ε ε (2 ε

t E 3 σ 4

ε ) ε (2 d

ε ) (ε ε ) ε (2 t E 3 σ 4

a v o

v a v o

rm m

a v o

3 a v a v o

am m

+ +

+ + +

− +


− +



where to is the initial thickness of the membrane, εa and εv are the axial and volumetric strains in the specimen, do is the initial diameter of the rubber membrane and the other parameters are the same as in Eq. (4.3).

The compression modulus Em was measured using the method recommended by Bishop and Henkel (1962). Hoop specimens of 25 mm width were taken from the supplied membranes whose thickness varied between 4.5 and 6 mm. For the computation of the membrane correction by Kuerbis and Vaid (1990) method a constant compression modulus of 126.58 kN/m was used, which was estimated for a membrane having an initial average thickness of 6 mm. Preliminary tests were then performed at lower and higher levels of confining pressure to determine which method should apply in this study. It was observed that at a very low level of confining pressure (σ′3 = 1 kPa) the difference between the two methods was 3.5 % approximately, with the Henkel and Gilbert (1952) method resulting in higher correction. However, the difference increased to 7.5 % for tests carried out at a higher confining pressure (σ′3 = 240 kPa), with the Kuerbis and Vaid (1990) method giving a higher correction. The corrected deviator stresses using the two methods are presented in Figure 56 for tests run at both the lower and higher confining pressures.