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									New Hollow Cylinder Torsional Apparatus (HCTA)                 Sergio Valdueza Lozano




                                            To my parents, for being so patient.
New Hollow Cylinder Torsional Apparatus (HCTA)                                                   Sergio Valdueza Lozano



      Contents.
      1. Abstract ........................................................................................................... 3
      2. Introduction ..................................................................................................... 4
            2.1. The rotation of principal stresses ......................................................... 4
            2.2. Liquefaction and anisotropy ................................................................ 6
            2.3. Historical review.................................................................................. 7
      3. Objectives ........................................................................................................ 9
      4. Description of the new HCTA in Bristol ......................................................... 10
            4.1. Sample dimensions .............................................................................. 12
            4.2. Loading system .................................................................................... 12
            4.3. Measurement system ........................................................................... 13
            4.4. Control panel ....................................................................................... 20
            4.5. Data control and monitor systems ....................................................... 22
      5. Sample fabrication ........................................................................................... 25
            5.1. Improvements in the sample preparation ............................................ 27
      6. State of stresses ................................................................................................ 28
      7. Results ........................................................................................................... 32
            7.1. Repeatability ........................................................................................ 35
            7.2. Triaxial compression ........................................................................... 36
                  7.2.1. Results and main features of each test ..................................... 37
                  7.2.2. Pictures of failure..................................................................... 42
            7.3. Pure torque........................................................................................... 43
                  7.3.1. Results and main features of each test ..................................... 44
                  7.3.2. Pictures of failure..................................................................... 47
      8. Conclusions ..................................................................................................... 48
      9. Acknowledgements ......................................................................................... 50
      10. References ..................................................................................................... 51




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  New Hollow Cylinder Torsional Apparatus (HCTA)                                     Sergio Valdueza Lozano



         1. Abstract.

          Many geotechnical problems involve the rotation of principal stress and strain directions in the
ground. To assess the fundamental behaviour of soils under such conditions, a Hollow Cylinder Torsional
Apparatus (HCTA) with independent controls and accurate measurements of the component stresses and
strains is required. The crucial characteristic of this apparatus is the possibility of combining axial load,
torque and internal and external pressures in a controlled way. These four elements can generate every state
of stress-strain in a hollow cylinder specimen.

         An experimental testing programme on Hostun sand has been proposed using a Hollow Cylinder
Torsional Apparatus. Behaviour characteristics in the small strain and medium strain domains under the
complex stress states, which are accessible with this apparatus, will particularly be explored. An accurate
evaluation of soil stiffness for this strain domain is essential when prediction of instantaneous deformation of
ground and displacement of structures under seismic loading are considered.

          For these purposes, the Hollow Cylinder Torsional Apparatus of Bristol will be upgraded. This
upgrading has been designed to be developed in three phases. At the end of the third phase, fully independent
measurements of stress and local systems of measurement of strains will be developed in order to allow
sensitive and accurate stress and strain measurements in the small strain domain. The apparatus will also be
adapted to follow the loading up to large strains and a new computerised control system will be achieved. In
order to validate the apparatus and to explore its full limits, an extended testing programme on Hostun sand
up to failure will be performed.

         With this project has been concluded the first phase of upgrading-validating. This phase involves the
construction of the apparatus in order to start a first series of tests under dry conditions. That consists of
building the main structure of the apparatus, setting the main transducers to control forces and displacements,
configuring the hardware and software to get and display the data received from the transducers, defining a
good sample preparation with a good repeatability, and developing a few dry tests that will show the response
of the apparatus.

         The report presents first a description of the Hollow Cylinder Torsional Apparatus used in the
Geotechnics Laboratory of the University of Bristol. It is described its main physical characteristics, how
loads are applied to the sample, the transducers and their calibration and resolution, and how the response of
the sand is obtained as well as the control of the parameters. Then it is explained the sample preparation. It
includes some advice to improve it for the next phases. It is also defined the state of stress-strain that occurs
in the sample. In this chapter, explanations about equations and constitutive laws used are included. Finally,
there are presented some triaxial compression tests and pure torque tests, which are carried out in dry
conditions and with different densities of Hostun sand.

         The main objective of the thesis is to learn how to work in a laboratory. This involves small things
like to choose the pieces that are missed in the apparatus, and to order them; or acquire the software needed
for the computer system; or simply to deal with the daily problems, and solve them. Furthermore, the
development of a high technical apparatus as the HCTA allows to control successfully other simpler
apparatus. Further aims of this project were to identify the limitations of the apparatus and to suggest some
solutions so that the Bristol Hollow Cylinder Torsional Apparatus (HCTA) can be improved.

       Finally, the tests done proved that the apparatus responds satisfactorily and it seems that its
development can be carried on.




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 New Hollow Cylinder Torsional Apparatus (HCTA)                              Sergio Valdueza Lozano



       2. Introduction.
        The purpose of any soil mechanics apparatus in a laboratory is to duplicate the in-
situ conditions. So far the most important tests used in Soil Mechanics, as Palomero J.
referred, are:
                            - the oedometer test
                            - the direct shear box test
                            - the true triaxial test
                            - the plain strain test
                            - the axisymmetric-triaxial test

        However, none of these apparatus can control the rotation of the principal stress-
strain directions. Axisymmetric triaxial tests cannot model these conditions ( can only be
0° or 90°) and conventional shear tests rotate the axis associated to 1 but without the
possibility of monitoring stress conditions.

        Nowadays there is a real need to study the behaviour of soil under stress rotation.
The HCTA is the only testing device capable of controlling the rotation of principal stress
directions.


       2.1. The rotation of principal stresses.

        In nearly all geotechnical problems, principal stress directions gradually rotate
along a slip surface. For example, in the case of an embankment, the directions of principal
stresses vary along a potential failure surface under sloping ground (figure 1).



                                                                          embankment



           Slip surface                                                ground




                                                                   Compression test

                                             Direct simple shear
                          Extension test     test




        Figure 1. Relevance of laboratory shear tests to shear strength in the field.
                                      (after Bjerrum, 1973).




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 New Hollow Cylinder Torsional Apparatus (HCTA)                            Sergio Valdueza Lozano


       As shown on figure 1, we use a relevant test for each part of this slip surface
(Bjerrum 1973):
   -     Under the embankment, shearing is induced by increasing the vertical stress. So a
         compression test is more appropriate.
   -     Where there is no increase in vertical or horizontal stresses, we can use a direct
         simple shear test.
   -     Finally, at the end of the slip surface, shearing is induced by increasing the
         horizontal stress. So an extension test can be made.


        However, it is obvious that there is a problem to choose which test enables to
establish the ground strength. There is a need to understand and to duplicate what happens
all along the failure surface because such stress rotations influence the behaviour of the soil
and lead to a spectrum of responses and deformations (figure 2).




       Figure 2. Influence of the direction of major principal stress on undrained sand.
                                     (After Vaid et al, 2002)


             -  is the rotation of1 with the vertical direction.
             - b is a sizing ratio for the magnitude of the intermediate principal stress relative
             to the magnitude of the major and minor principal stresses.

                                                            
                                                                 '     '

                                 0  b 1                b     2     3

                                                            
                                                                 '     '
                                                                 1     3




       If b is kept constant, Vaid has shown (figure 2) that deformation depends on the
value of , which can goes from 0 to 90. These responses go from strain hardening, when
is equal to 0, to strain softening, when  is equal to 90.



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 New Hollow Cylinder Torsional Apparatus (HCTA)                        Sergio Valdueza Lozano


        The HCTA is the only testing device capable of imposing three dimensional stress
states, and it can rotate the principal stress directions. In this apparatus, one can apply and
control independently the principal stresses ,  and 3 and the rotation  of 1 with the
vertical direction. These constitute four parameters that influence soil behaviour and so we
can study the effects of each one on the soil behaviour.


        Yet it is not a common practice in Soil Mechanics because of experimental
difficulties. Indeed, it is hard to duplicate and to control changes in the magnitude and
direction of the principal stresses. Bishop & Henkel (1962) have referred these difficulties.

        The rotation of the principal stress directions exists also when loads over the soil
are cyclic, or when different loading are applied to the ground. Such real situations can
take place, for example, under offshore platforms subjected to cyclic vertical and
horizontal forces (waves) as shown on figure 3. Tunnels, foundations, tall buildings under
wind loads as well as dams lead to rotation of principal stress. During an earthquake as
well, a major part of the soil deformation may be attributed to the upward propagation of
shear waves from underlying layers and the orientation of principal stress and strain
directions changes continuously.




                            Figure 3. Stress under cyclic waves.


       2.2. Liquefaction and anisotropy.

       Another aspect of the HCTA is to study inherent or induced anisotropy. Inherent
anisotropy is due to fabric deposition and the induced one is due to the evolution of the
application of stresses and strains.


       Liquefaction can be studied as well. It can be triggered by either static or cyclic
loading (e.g. Saada, 1988; Ishibashi & Sherif, 1974; Muramatsu & Tatsuoka, 1981).
Generally, these investigations have sought to simulate field conditions during earthquake
loading (see figure 4).




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 New Hollow Cylinder Torsional Apparatus (HCTA)                       Sergio Valdueza Lozano




                Figure 4. Mohr circles for continuously rotating principal stresses.
                                       (after Saada, 1988)



       2.3. Historical review.

       It was in the 30s when the idea of combining axial and torsional stresses on a
hollow cylinder appeared for the first time to test soils.

       Cooling and Smith (1936) were the first in performing tests applying axial and
torsional stresses on unconfined hollow cylinder samples.

        Confined hollow cylindrical specimens were used in the 60s by Broms and
Casbarian (1965), who used them to study the rotations of principal stresses. Saada (1967,
1968, 1969) and Lomise et al. (1969) published articles related to the use of hollow
cylindrical specimens.

        Yoshimi and Oh-Oka (1973) and Ishibashi and Sherif (1974) conducted several
studies based on torsion and shear stresses on short hollow cylinder specimens in order to
obtain a uniform distribution of shearing strain under torque. Even though their
investigations have not been designed to study the effects of the rotation of principal
stresses, they have tried to duplicate real conditions like earthquakes.

       Lade (1975) presented the results of tests carried out with hollow cylinder
specimens on sands to analyse the behaviour under rotational forces. Hardin and Drnevich
(1972) used hollow cylinders to study shear modulus and damping ratios in different soils.
Tatsuoka et al. (1982) studied the behaviour of dense sand with a hollow cylinder device.



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 New Hollow Cylinder Torsional Apparatus (HCTA)                      Sergio Valdueza Lozano


        Hight et al. (1983) made a very complete study about the hollow cylinder apparatus
and the effects of the principal stress rotation. The same authors published (Symes et al.,
1984) the results of several tests on sands in order to study the principal stress rotation.
These researchers, from the Imperial College of London, were the first in testing hollow
cylinders with different external and internal pressures. Also Miura et al. (1986) conducted
tests on sand with a hollow cylinder apparatus using the ideas from the Imperial College to
get rotation and be able to change the values of the intermediate principal stress.

       Tatsuoka et al. (1986) studied the behaviour of sands. More recently, many other
authors have researched with the HCTA and this has become widely recognised as a useful
apparatus with reliable results. Also Karchafi (1988) carried out his thesis and contributed
the HCTA became more known.

       Saada (1988) wrote a paper stressing the importance of the development of the
hollow cylinder torsional apparatus for Soil Mechanics investigation and he also discussed
the advantages and inherent limitations.

       Last years, other researchers have worked with the HCTA: Sayao and Vaid (1991),
Ishibashi et al. (1996), Nakata et al. (1998), Zravkovic and Jardine (1997, 2001).




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 New Hollow Cylinder Torsional Apparatus (HCTA)                       Sergio Valdueza Lozano



       3. Objectives.
        The main objective is to participate in the first phase of the construction of a
Hollow Cylinder Torsional Apparatus (HCTA). At the end of the three phases of the
project the apparatus will have the widest range of work, being able to make static or
dynamic tests and to acquire precise results for small strains as well as for large strains.

       More specific objectives for the first stage of development are:

              To get used with laboratory works, solving all the daily problems with
           missing pieces, orders, etc.
              To calibrate and install the main transducers for forces and displacements.
              To learn how to control and read the parameters involved in the tests (use of
           Dartec and Labview, respectively).
              To finish the construction of the apparatus building the control panel for the
           water and air nets.
              To get a sample preparation with good repeatability.
              To manage to use air pressure inside belloframs to control axial force and
           torque.
              To make some tests of Hostun Sand samples in dry conditions in order to
           validate the apparatus.




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 New Hollow Cylinder Torsional Apparatus (HCTA)                       Sergio Valdueza Lozano



       4. Description of the new HCTA in Bristol.
        Figure 5 shows the configuration of the New Hollow Cylinder Apparatus in
Bristol. The hollow cylinder sample is enclosed in a confining pressure chamber, so the
basic setup is very similar to the triaxial compression apparatus, but adding the torque
mechanism.

        The sample used in the new HCTA has an outside diameter of 100 mm, 20 mm of
wall thickness and a height of 200 mm, and it is enclosed between two flexible rubber
membranes 0’3 mm thick. The sample is kept between two porous stones. The porous
stones provide the drainage and they are protected from the samples with filter papers. The
specimen is supported by a stainless steel base, which works as a sample pedestal, and is
connected to the top with another stainless steel cap. These caps, top and bottom, are also
used to seal the inner and outer rubber membranes of the sample with O-rings. To apply
the loading to the sample the top cap is linked to the loading system by means of a stainless
steel connector.

        The 200 litres confining pressure chamber has an overall height of 96 cm, and a
diameter of 60 cm. Twelve stainless steel tie bars, 13 mm in diameter, provide reaction to
the cell pressure. The chamber can resist a maximum pressure of 700 KPa.




 Figure 5. Physical description of the HCTA.             Picture 1. New HCTA.




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New Hollow Cylinder Torsional Apparatus (HCTA)                      Sergio Valdueza Lozano




   Picture 2. Bottom base (front view).          Picture 3. Bottom base (aerial view).




     Picture 4. Top cap (front view).              Picture 5. Top cap (aerial view).




    Picture 6. Connector (front view).            Picture 7. Connector (aerial view).




                                 Picture 8. Porous stone.




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 New Hollow Cylinder Torsional Apparatus (HCTA)                        Sergio Valdueza Lozano


       4.1. Sample dimensions.
        The uniformity of the stress distribution in the hollow cylinder is affected by its
geometry. Frictional forces are developed at the ends of the specimen, but they can be
dismissed as one move away from the end platens. In addition, the inner and outer
membranes that contain the sample can affect the results in two more ways: the
axial/torsional resistance of the membrane; and the membrane’s penetration by the grains,
whose influence is related to the particle size for granular material and to the pressure in
the cells (Saada, 1988). More recently, Sayao and Vaid (1991) also analysed the geometry
of the specimen. The stress non-uniformities due to the specimen curvature and end
restraint were limited to acceptable levels, so the following recommended dimensions were
reached:

               - Wall thickness:      Re-Ri = 20 to 26 mm.
               - Inner radius:        0’65  Ri/Re  0’82
               - Height:              1’8  H/(2*Re)  2’2

      The values of the new HCTA in Bristol, with Re = 50 mm and Ri = 30 mm, are
inside or really close to these limits.


       4.2. Loading system.
       The axial and torque loading can be transmitted in two different ways:
hydraulically or pneumatically.

        The hydraulic system is set above the pressure chamber, and is mainly important to
study the dynamic behaviour of the soil, which involves a range of very small
deformations. However, the two servo hydraulic actuators provide compression/extension
and torsion in dynamic and static conditions, with a capacity of 10 KN and 400 Nm
respectively. The hydraulic system is connected to a controller system (DARTEC) that,
with a computer that uses specific software, applies and controls the force and torsion by
means of loads as well as by means of strains.

        In this research report, only the pneumatic system is used. Its situation is under the
pressure chamber. The axial load, F, on the specimen is applied by means of a diaphragm
air cylinder bellofram, while the torque load is applied by means of the combination of two
diaphragm air cylinders. The axial load is controlled increasing or decreasing the air
pressure inside the cylinders. This pressure is regulated with a standard pressure regulator.
The torque is more difficult to control, and it has been applied two different methods.
Firstly, one of the two belloframs was left free and the pressure was applied to the other
cylinder, so the sample is rotated in one direction. To rotate the sample in the other
direction, just it was enough to interchange the function of the cylinders. With this method
the sample rotated too quickly, so it was realised that there was hardly control of the
pressure. The second method improves this lack of control: the two belloframs are under a
higher pressure than one atmosphere, which is controlled with two standard air pressure
regulators. The sample is in equilibrium meanwhile the pressure in both cylinders is the
same. To apply a torque to the sample it is only necessary to increase or decrease a bit the
pressure in one of the belloframs. As slower the pressure is increased or decreased, more
control is achieved in the application of the torque.



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 New Hollow Cylinder Torsional Apparatus (HCTA)                      Sergio Valdueza Lozano




     Picture 9. Pneumatic system.           Picture 10. Pneumatic torque system.


       4.3. Measurement system.
        The new HCTA of Bristol is designed to use 15 transducers. In the first phase of
development, only three of them have been installed: a load cell that measures force and
torque, a linear variable differential transformer (LVDT) for axial strain, and a rotary
capacitive displacement transducer (RCDT) for the rotation of the sample.

       The transducers that will be installed in a second phase of the development are
three pressure gages for the inner, outer and pore pressures; and two volume change
devices that measure the volume change of the sample and inner cell.

       After that, six non-contact sensors get the small axial, radial, circumferential, and
shear displacements; and one LVDT measure the change of the inner diameter of the
sample. These seven transducers are internal instrumentation to the sample; the others are
considered external instrumentation.

        Both external and internal systems of measurement have advantages and
limitations. External measurements increase bedding, seating and tilting errors in
displacements and loads; but internal instrumentation adds more difficulties in the
mounting solutions, plus more restrictive limits to the sample’s dimensions. Vaid et al.
(1990) conclude that there are no significant differences using external instrumentation if
appropriate care was taken to eliminate bedding, seating and (or) tilting errors. In this
work, the author was able to identify some of these limitations, eliminating them when it
was possible.

       Load cell (2 components model, type 49030). Load cells are highly stressed devices
and commonly have safety factors between two and five times rated capacity under static
conditions. Fatigue applications and environmental factors can contribute to reducing this
margin. The load cell in the HCTA of Bristol is situated above the top cap (see figure 7 in
chapter 4.4), inside the pressure chamber. Its ranges are 8000 N and 400 Nm, in axial force
and torsion, respectively. It has an excitation voltage of 10 Volts DC. In the chart 1 and


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 New Hollow Cylinder Torsional Apparatus (HCTA)                                              Sergio Valdueza Lozano


chart 2, it is showed the calibration of the load cell for the axial force and the torsion,
giving calibration factors of 352.66 N/mV and 24.133 Nm/mV, respectively. The supplier
of the load cell provided these calibration curves.



                                       Axial Force (Calibration Load Cell)
                                                            Data        Linear (Data)


                        8000
                                                   y = 352.66x + 0.5878
          Force (N)




                        6000                              R2 = 1
                        4000
                        2000
                              0
                                  0            5                   10                   15               20

                                                              Voltage (mV)



                                          Chart 1. Axial force calibration.



                                          Torsion (Calibration Load Cell)
                                                            Data        Linear (Data)


                        500
         Torsion (Nm)




                                      y = 24.133x - 0.077
                        400
                                             R2 = 1
                        300
                        200
                        100
                          0
                              0               5                    10                   15               20

                                                             Voltage (mV)



                                             Chart 2. Torsion calibration.


        LVDT (model 3258-50). Linear Variable Differential Transformers are a popular
technology for measuring position. The measurement with LVDT is performed without
any mechanical contact between the movable component of the sensor (plunger) and the
measuring coils. They have the advantage working on a simple and rugged principle and
producing a signal that is linearly related to position. The LVDT used to measure axial
strains has a range of 50 mm and an excitation voltage of 5 Volts DC. Figure 7 in chapter
4.4 shows the position of the transducer in the HCTA during the test. Chart 3 and chart 4
show the calibration for this transducer carried out before the start of the tests, which is
divided in two slopes: going up from 0 to 25 mm, and going down from 50 to 25 mm. The
average of the calibration factor obtained was of 2.82955 mm/mV.



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 New Hollow Cylinder Torsional Apparatus (HCTA)                                                    Sergio Valdueza Lozano



                                                 LVDT 3258-50 5Volts 0-25mm
                                                               Data            Linear (Data)
          Displacement (mm)
                              30
                              25                   y = 2.8389x + 0.4515
                              20                         R2 = 1
                              15
                              10
                               5
                               0
                                   0   1          2       3        4             5        6    7         8       9

                                                                  Voltage (mV)



                                       Chart 3. Calibration LVDT from 0 to 25 mm.



                                                LVDT 3258-50 5Volts 50-25mm

                                                               Data            Linear (Data)
         Displacement (mm)




                              55       y = 2.8202x - 1.0507
                              50
                              45                R2 = 1
                              40
                              35
                              30
                              25
                              20
                                   8       10            12               14             16         18          20

                                                                  Voltage (mV)



                                       Chart 4. Calibration LVDT from 50 to 25 mm.


        RCDT (model RCDT300 2344). Rotary Capacitive Displacement Transducers use
a non-contact capacitance based sensor to measure shaft position. One of the main
advantages of the RCDT is that there is no physical contact across the sensing element.
The full-scale range is from 0 to 300º, and the excitation voltage is of 15 Volts DC. The
position of the transducer during the tests is showed in figure 7 (chapter 4.4). Chart 5,
chart 6 and chart 7 show the calibration for this transducer carried out by the author,
which is divided in three slopes: two going up from 0 to 360º, and one going down from
360 to 0º. All the calibration is done by steps of 10º. The charts show that the response is
not perfect linear, this is due to small deviations of the 10º when the steps are applied, and
it is not due to a bad behaviour of the transducer. The average of the calibration factor
obtained was of 0.09533 º/mV. As the RCDT is absolute, data is accurate from switch on
and there is no need for repeated zero referencing.




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New Hollow Cylinder Torsional Apparatus (HCTA)                                           Sergio Valdueza Lozano



                                     RCDT300 2344 15Volts 0-360 (1)
                                                      Data        Linear (Data)

                    350
                    300
                    250              y = 0.0955x - 137.11
          Degrees

                    200                   R2 = 0.9994
                    150
                    100
                     50
                      0
                      1000     1500         2000        2500          3000      3500     4000    4500

                                                        Voltage (mV)



                             Chart 5. Calibration RCDT from 0 to 360º (1).


                                     RCDT300 2344 15Volts 0-360 (2)
                                                      Data        Linear (Data)

                    350                          y = 0.096x - 60.122
                    300                              R2 = 0.9997
                    250
          Degrees




                    200
                    150
                    100
                     50
                      0
                       250     750        1250      1750       2250      2750     3250    3750   4250

                                                           Voltage (mV)



                             Chart 6. Calibration RCDT from 0 to 360º (2).


                                       RCDT300 2344 15Volts 360-0
                                                      Data        Linear (Data)

                    350                y = 0.0945x - 75.387
                    300                     R2 = 0.9994
                    250
          Degrees




                    200
                    150
                    100
                     50
                      0
                      1000     1500         2000        2500          3000      3500     4000    4500

                                                           Voltage (mV)



                              Chart 7. Calibration RCDT from 360 to 0º.


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 New Hollow Cylinder Torsional Apparatus (HCTA)                                        Sergio Valdueza Lozano


       Time-stability response of the transducers.

        These four transducers have been tested to get their accuracy. They were kept
during the night working for 17 hours in a fix position. Charts 8 to 11 show different
behaviours for each transducer. There are two main kinds of variations to be studied. One
is the variation of the value from one data to the next, or the standard deviation of the
measured value. The other issue is the variation of the value with time. The testing has
been done without control of the temperature, so it is probably that the second kind of
variation is due to slightly changes on temperature in the laboratory.

         The LVDT presents the largest standard deviation. In chart 8 it is showed a
resolution of +/- 0.005 mm. That means that, comparing this value with the common
displacement measured in the peak of the tests (20 mm), the relative error is 0.05 %.
Despite this small value, the standard deviation is the largest found. The point is that,
statistically in time, there is data that goes quite far away from the average. In the other
hand, there is a good stability with time: the value only changes 0.01 mm every 25 hours.



                                                   Resolution LVDT 3258-50

                             0.00

                             -0.01
         Diaplacement (mm)




                             -0.02

                             -0.03

                                         y = -0.0004x - 0.0193
                             -0.04             2
                                             R = 0.1289
                             -0.05
                                     0                5              10           15                20
                                                                 Time (hours)


                                              Chart 8. Resolution LVDT 3258-50.


        The RCDT presents a resolution of +/- 0.05 degrees. That means that, comparing
this value with the common rotation measured in the peak of the tests (50 degrees), the
relative error is 0.2 %. However, there is change of the value with time: 0.1 degrees every
13.8 hours.




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 New Hollow Cylinder Torsional Apparatus (HCTA)                                                     Sergio Valdueza Lozano



                                                                 Resolution RCDT300 2344

                                           0.15
                                           0.10
                      Rotation (degrees)   0.05
                                           0.00
                                           -0.05
                                           -0.10
                                           -0.15
                                           -0.20                                             y = 0.0072x - 0.1203

                                           -0.25                                                   R2 = 0.4478

                                           -0.30
                                                   0                 5               10            15                 20
                                                                              Time (hours)


                                                       Chart 9. Resolution RCDT300 2344.

        The load cell has very similar behaviours for both axial and torque load. The
resolution is very good. The maximum deviation between one value and the next is 0.4 N
for the axial load and 0.1 Nm for the torque load. The relative errors obtained, comparing
with the maximum force and torque measured, are 0.05% and 0.67%, respectively.
However, the error in the load cell is introduced cause a change of the value with time.
This change is of 3.7 N each 10 hours for the axial load and of 0.5 Nm each 10 hours for
the torque load.


                                                         Resolution Load cell (Axial load)

                              2.00

                              0.00

                       -2.00
         Force (N)




                       -4.00

                       -6.00
                                                   y = -0.3703x - 1.1356
                       -8.00                           R2 = 0.9283
                     -10.00
                                              0                 5               10            15                 20
                                                                           Time (hours)



                                                   Chart 10. Resolution Load cell for axial load.


                                                                                                                           18
 New Hollow Cylinder Torsional Apparatus (HCTA)                                                  Sergio Valdueza Lozano




                                              Resolution Load cell (Torque load)



                       0.20
         Torque (Nm)




                       -0.30


                       -0.80

                                     y = -0.0578x - 0.2488
                       -1.30
                                          R2 = 0.922

                       -1.80
                                0                         5                        10       15               20
                                                                          Time (hours)



                                     Chart 11. Resolution Load cell for torque load.


         However, the fact of working with differences or relative values and that the tests
last as much ten minutes, makes the error induced for the changes on time irrelevant.
Therefore, the standard deviation is the value that shows the resolution of a transducer, and
its relative value gives its magnitude. According to this, the most precise data recorded is
the axial displacement and the axial force, meanwhile the least precise is the torque.

        Using the formulation given in the chapter 5 the resolutions can be transformed
into the values of minimum stresses and strains you can measure and, therefore, control.
These values are the following:


                                       F
                               
                                      R  R   P  0.08 KPa 1  1.08 KPa
                                    
                            z             2       2
                                          e       i


                                           2M *  R  R  
                                                           
                                     
                                          R  R  
                                                              T            e            i
                                      z               2
                                                      4
                                                             0.47 KPa
                                                                  4
                                                      e          i

                                                  H 
                                                      0.005 %
                                                          z
                                                   H
                                                    
                                          2 R R   0.0036 %
                                                                      3    3
                                                                      e    i
                                                                      2        2
                                            3H R R                    e        i




                          (See figure 10 in chapter 6 for the definitions of parameters)

                                                                                                                      19
 New Hollow Cylinder Torsional Apparatus (HCTA)                                                Sergio Valdueza Lozano


       4.4. Control panel.
        The next figures and pictures show the main elements of the control panel and its
connections with the HCTA. The panel is built to control the air and the water pressures,
and to install the volume change transducers.


                    De-aired water cell
                                             Valve                         Pressure gauges



                                                      (o)            (i)         (u)
             Magnetic stirrer
                                                                                             Hydraulic System




                                                                                              Vacuum system
                                     V
                                     (u)




                                                      Pressure
                Volume change        V               regulators
                                     (i)
                                                (o)                (i)                 (u)




                                                      Air-water pressure interchange
                      Transducer




                                           Figure 6. Control panel.




                                Picture 11. Front view of the control panel.


                                                                                                                    20
                                                                                                                                                                                                        AIR VACUUM
                                                                                                  System                                                 AIR SUPPLY
                                                                                                Chargement                                          P                                                   AIR
                                                                                LABVIEW                                                                  COMPRESSOR
                                                                              (back pressure)
                                                                                                 Hydraulic
                                                                                                             Load cell                                                                                  WATER
                                                                                                                   Back pressure                                                                        LABVIEW (experimental data)
                                                                   LABVIEW
                                                                                                                                                 De-aired water cell
                                                              (axial force & torque)
                                                                                                                           Magnetic stirrer
                                                                                                                                                                       Valve          Pressure gauges
                                                             Inner pressure
                                                                                                                                 P
                                                                                                                                                                               (o)             (i)             (u)
                                                                                                                                                                                                                           Hydraulic
                                                                                                                                                                                                                            system
                                                             Outer pressure
                                                                                                                                                                        SCH              SCH             SCH
                                                                                                                                                                                                                                       New Hollow Cylinder Torsional Apparatus (HCTA)




                                                                                                                                                            V                                                             Vacuum
                                                                                                                           LABVIEW                          (u)                                                            system
                                                                                                                         (outer pressure)


                                                                   LABVIEW
                                                               (axial displacement)

                                                                   LVDT                                                                     Volume                               Pressure
                                                                                                                                                            V
                                                                                                                                            change                               regulators
                                                                                                                                                            (i)
                                                                                                                                        LABVIEW                          (o)                   (i)                   (u)
                                                                                                                                      (inner pressure)
                                                                     LABVIEW
                                                             (rotational displacement)




     Figure 7. Connections between HCTA and control panel.
                                                                    RCDT                                                                    Transducer                         Air-water pressure interchange
                                                                                                                                                                                                                                       Sergio Valdueza Lozano




21
 New Hollow Cylinder Torsional Apparatus (HCTA)                      Sergio Valdueza Lozano


       4.5. Data control and monitor systems.
        The new HCTA of Bristol use two informatic systems to control, to monitor and to
record the changing parameters of the tests: DARTEC and Labview.

       As it has been said before, the DARTEC system controls the axial and torsional
actuators of the hydraulic system, and its use is optional.

        The Labview uses the data transmitted from the Datascan 7220, an intelligent input
output analog module designed for real time measurement, data collection and
communication. In other words, the Datascan is a scanner apparatus that reads the data
from the transducers in voltage and converts it into a digital signal to the computer. The
table 1 shows the specification of this analog module (the features in italic format are the
ones used with the HCTA). The Labview just take this data and operate with it to get
depurated values, to monitor them in the computer’s screen and, if required, to record
them. Figure 8 and figure 9 shows how the data is got and modified, and how it is
monitored in the screen.




                                                                                          22
    New Hollow Cylinder Torsional Apparatus (HCTA)                             Sergio Valdueza Lozano




                  Input            Input
 N of inputs                                     Resolution                     Sensors supported
                impedance         current
                                              16 bits @ 40 rdgs/s
     16           30 M             5 A                               DC Voltage, Thermocouples and Current
                                              14 bits @ 400 rdgs/s
                                             Sensivity
Sensor type       Ranges                                                             Accuracy
                                   16 bit           14 bit
 DC Voltages        10 V           320 V          1.28 mV               +/- 0.02 % rdg +0.01% range + 1bit
                   1.3 V            40 V          160 V                +/- 0.02 % rdg +0.01% range + 1bit
                  150 mV            5 V            20 V                +/- 0.02 % rdg +0.01% range + 1bit
                   20 mV          0.625 V          2.5 V           16 bit (+/- 0.02 % rdg +0.01% range + 5V)
                                                                     14 bit (+/- 0.02 % rdg +0.01% range + 10V)
Thermocouples

   K type       -100 to 500 C      0.02 C            0.1 C                             0.9 C
                500 to 1200 C      0.2 C             1.0 C                             1.2 C
                1200 to 1600
                                   0.2 C             2.0 C                             5.0 C
                      C

    J type      -50 to 360 C       0.02 C            0.1 C                             0.9 C
                360 to 800 C       0.2 C             1.0 C                             1.1 C

   T type       -150 to 400 C      0.02 C            0.1 C                             0.9 C

   R type        0 to 1600 C       0.1 C             0.4 C                             2.0 C

   S type        0 to 1600 C       0.1 C             0.4 C                             2.0 C

   E type       -50 to 290 C       0.2 C             0.1 C                             0.9 C
                290 to 1000 C      0.1 C             0.4 C                             1.3 C

   B type       200 to 1600 C      0.5 C             2.0 C                             5.0 C

   N type       - 200 to 100 C     0.1 C             0.4 C                             1.2 C
                100 to 580 C       0.05 C            0.2 C                             1.0 C
                580 to 1300 C      0.1 C             0.4 C                             1.2 C

   Current

  4 to 20 mA     4 to 20 mA                                                           +/- 0.15%



                                 Table 1. Datascan 7220 specification.




                                                                                                      23
New Hollow Cylinder Torsional Apparatus (HCTA)                  Sergio Valdueza Lozano




                           Figure 8. Diagram panel (Labview).




                            Figure 9. Front panel (Labview).



                                                                                     24
 New Hollow Cylinder Torsional Apparatus (HCTA)                        Sergio Valdueza Lozano



       5. Sample fabrication.

        Three screws hold the inner membrane and the base plate on the bottom base.




    Some talcum powder is                                           The three parts of the outer
applied on the inner mould to                                       mould are assembled and 6
   slip it well into the inner   The outer membrane is put
                                                                    screws fix it. The vacuum
  membrane, and some filter      with 2 rings that fix it on the
                                                                   pipe is connected to stick the
 papers are placed to prevent            bottom base.
                                                                   outer membrane on the outer
   sand from damaging the                                                     mould.
          porous stone.




                                                                                            25
  New Hollow Cylinder Torsional Apparatus (HCTA)                      Sergio Valdueza Lozano




    After fixing the outer
membrane with 2 rings at the       The same quantity of sand is placed 4 times. The weight of
 top, the vacuum is applied          sand depends on the density. The 4 layers are tamped
  between outer mould and                identically, so the sample has uniform density.
      outer membrane.




                                  After   fixing    the    inner
                                  membrane with a ring, the
When all the sand is inside the
                                  vacuum between the outer
sample, some filter papers are                                   The connector is installed, but
                                  mould     and    the     outer
placed on the top plate, and 2                                   paying attention to the
                                  membrane is stopped. Now
rings fix the outer membrane                                     horizontality.
                                  the vacuum is applied through
on this top plate.
                                  the sample. The inner mould
                                  is removed.




                                                                                           26
New Hollow Cylinder Torsional Apparatus (HCTA)                      Sergio Valdueza Lozano




                                Finally, the outer mould is
                                         removed.




      5.1. Improvements in the sample preparation.

  -   It has been noticed that the vacuum applied between the outer mould and the outer
      membrane was not enough to stick the membrane on the mould, especially with
      dense sand. A solution could be to do some more holes through the outer mould.
  -   There is a gap between the porous stone and the outer membrane at the bottom and
      the sand can go through. It would help to put some tape on the outer mould, and to
      reduce the internal diameter of the mould.
  -   When the sample is in place, it is quite difficult to check the horizontality because
      there is a lack of space between the connector and the HCTA load cell. In the
      chapter 7.1 it is given a possible solution to this problem.
  -   There are some problems of anisotropy in the sample, when the sand is poured and
      tamped. The technique of pluviation could lead to better results. This technique
      improves the arrangement of the sand, being more homogenous, so it is possible to
      obtain the same sample without experimental input of the engineer.

     Actually, the target was not to study the response of the sand, so the issue was not
 to have a perfect sample preparation. The aim was to validate the HCTA. Meanwhile
 doing this, the author has reached a good experience in improving the sample
 preparation.




                                                                                         27
 New Hollow Cylinder Torsional Apparatus (HCTA)                                                                Sergio Valdueza Lozano



       6. State of stresses.

         The most important issue in the HCTA is to control the rotation of the principal
stress-strain directions, so to simulate any special “stress path” that occurs in the field. That
control is possible subjecting the hollow cylindrical specimen to axial load F, torque M T,
and inner and outer pressures (Pi and Po). These four loading parameters generate stresses
(r, , z,  z) and strains (r, , z, ).




               Figure 10. Forces, stresses and strains on an element in the wall.

        The state of stress and strain achieved can be represented in cylindrical co-ordinates
by the following matrixes:


                   r                                                             r
                                    0            0                                                  0          0 
                                                                                                                     
                    0                      z                                0                    z 
                   0                                                             0
                                      z        z                                                   z    z  

                      
                       z       z                                                    z
                                                                                              z  
                                                                                                           2

        These matrixes can also be represented in terms of principal stresses and strains
using the following expressions:



                                                                        z    
                                                                                            2

                                           z
                                                                              
                                                                                                  2
                                                                                                  z
                                                                       2 
                                1
                                                 2

                                                               2       r


                                    z    
                                                                                            2


                              2          
                                                        z                                       2
                                                                                                  z
                                                                                           
                                3
                                                                              2
                                                   Principal stresses.


                                                                                                                                    28
 New Hollow Cylinder Torsional Apparatus (HCTA)                                               Sergio Valdueza Lozano




                                                             z    
                                                                                     2

                                          z
                                                                   
                                                                                         2


                                                            2 
                               1                                                         z
                                             2

                                                        2           r


                                   z    
                                                                                     2


                             2       
                                                 z                                     2
                                                                                         z
                                                                                    
                               3
                                                                           2
                                                 Principal strains.



        As it is pointed above, the radial stress r in HCTA tests is usually the intermediate
principal stress 2. Application of torque causes rotation () of stresses 1 and 3 in the
vertical plane perpendicular to the radial direction. The value of  can be computed
therefore from the known stress components , z and z:



                                         tg(2 )                          2   z

                                                                        z  


                       

                                                                            z

                                                 2               
                                   3                                    z 1                 


                 Figure 11. Mohr circle representation of stress in the wall.


        The interpretation of results from HCTA tests is made by considering the entire
specimen as a single element. The fact that this specimen has a wall thickness, and that the
stresses vary across this wall, make necessary to work in terms of averages of stress and
strain.




                                                                                                                   29
 New Hollow Cylinder Torsional Apparatus (HCTA)                                                             Sergio Valdueza Lozano


      The expressions used are based on equilibrium, strain compatibility, and with the
assumption that the work done by the applied forces and torques is equal to the sum of
work done by the stresses and strains involved.

                         d           r
                                                                                   d   1     0
                         dr
                                 r
                                                                  0
                                                                                      dr r 
                                                                                                              r
                                                  r
                         Equilibrium equation.                                        Strain compatibility.


      The average values of z and , and z and , are calculated using only equilibrium
equations or strain compatibility, respectively, so they are therefore independent of the
constitutive law of the material being tested. However, r is based on a linear elastic stress
distribution, and r and  are based on a linear variation of radial displacement across the
wall, so they are really related to the constitutive law of the material.

        It exists two different formulations to calculate z (Ishibashi et al., 1985; Palomero,
2002). When the soil’s behaviour is perfectly elastic, the torsional shear stress increases
linearly with the specimen radius; and when the soil behaves as a rigid plastic material, a
uniform shear stress distribution is assumed through the cross section of the specimen. The
selection between both formulations depends on the level of applied shear strain. The
elastic behaviour should be considered for small strains, and the plastic behaviour should
be considered for large strains. Meanwhile the values are only used to validate the
apparatus, and not to get soils parameters, the differences between both values are
negligible. For the sake of consistency, however, all stress components are computed by
assuming a single constitutive law: a linear elastic stress distribution. So it is assumed a
linear variation of z through the wall.



                                                                                                  Re
              P R P R                                                                                      Ri
                 
               R  R          o     e              i       i
                                                                                        
                     r
                                      e               i
                                                                                            r
                                                                                                R R   e            i


                                                                                             R R
                                                                                                  
            P R PR
                            o        e           i       i
                                                                                                     e                i

                R R                    e              i                                         R R   e            i

                                                                                                H
                                                                      2           2
             F      P R PR
                                                                                            
          R  R  R  R 
                                                          o           e       i   i
         z                   2            2                           2       2                    z
                             e            i                       e           i                   H
             2M *  R  R                                                                    2 R  R 
                                                                                                           3            3


                                                                                     
            R  R                                                                        3H R  R 
                                      T                           e       i                                e            i
             z         2       4            4                                                             2               2
                                e            i                                                             e               i



                         Stress parameters.                                                 Strain parameters.

                                     (See figure 10 for the definitions of parameters)




                                                                                                                                 30
 New Hollow Cylinder Torsional Apparatus (HCTA)                                  Sergio Valdueza Lozano


       When Pi = Po = P the stress expressions are:

                                                    r
                                                         P

                                                    
                                                         P

                                        F
                                     R  R   P
                                            
                                    
                                        z                    2       2
                                                             e       i


                                    2M *  R  R 
                                                  
                              
                                   R  R  
                                                         T               e   i
                                z             2 4
                                                                4
                                                 e              i



                      (See figure 10 for the definitions of parameters)

        Saada (1968) advise not to use different inner and outer pressures because this
leads to non-uniform stresses across the sample, which results in different axial strains due
to Poisson’s effect. However, this condition fixes the relationship between the parameter b,
which visualises the effect of 2, and , related to the inclination of principal stresses.

                                                b = sin2 

        Symes et al. (1985) justify the use of different inner and outer pressure through the
need of controlling these two parameters separately. The author considers that, being the
versatility of the HCTA one of its best features, the use of different pressures is widely
justified, but trying to consider the non-uniform strains caused by the non-uniform stresses.




                                                                                                      31
 New Hollow Cylinder Torsional Apparatus (HCTA)                        Sergio Valdueza Lozano



       7. Results.
        In order to validate the apparatus the research has been divided in three different
test campaigns: repeatability, triaxial compression tests and pure torsional tests.

       The main common feature of all the tests is that, as the full apparatus is still
incomplete, it has been impossible to use the water and therefore the sample is tested in dry
conditions. However, this means that the sample is confined with the same pressure inside
and outside, since the confinement of the sample before starting to load it has been
obtained applying vacuum to the sample (Po = Pi = Vacuum).

        The second main feature is that, as it has been explained before, the data has been
measured with just three transducers: one LVDT for the axial displacements, one RCDT
for the rotation of the sample, and a load cell to measure the force and torque. Therefore,
there is no data about the radial displacements of the sample, it is to say, there is no
information about the change of cross-sectional area of the specimen.

       In addition to this, it has been used a pressure gauge to keep permanently a control
of the vacuum applied to the sample. Due to this, the results are expressed in terms of
loadings and displacements/rotations, but not in the common parameters of stress/strains.
However, at the end of each test it is made a simplification considering that there is no
change in cross-area, so an approximation of the stress-strain values is given.

The sand used in the tests is denominated Hostun RF Sand. It is a type of manufactured
sand that is created by the crushing of larger particles such as rocks or boulders. Therefore,
its properties may vary depending on how it was manufactured. However for this study, its
properties were set and are shown in table 2.


                                          Hostun Sand
                          emin                                 0.65
                          emax                                   1
                          D50                                0.30 mm
                        Shape                               Sub-angular
                Particle sphericity, Sp                         0.6
            Coefficient of uniformity, Cu                        1.6
                  Specific gravity                              2.65

                              Table 2. Properties of the Hostun Sand.




                                                                                            32
 New Hollow Cylinder Torsional Apparatus (HCTA)                        Sergio Valdueza Lozano




       Figure 12 below shows the sub-angular shape of the sand viewed under an electron
microscope at a magnification 40 times.




                    Figure 12. Sub-angular shape of the Hostun Sand.


       The general grain distributions of Hostun Sand are shown in figure 13 in three
categories. The grain distribution of the sand that is used for this study is shown in red.




                       Figure 13. Grain distribution of Hostun Sand.




                                                                                            33
 New Hollow Cylinder Torsional Apparatus (HCTA)                                                     Sergio Valdueza Lozano


       The following formulation was used to get an approximate weight of sand for each
sample:

                                    e         e                                        P  m
                             ID                                                                 
                                        max                                                   s            s

                                            emin                         P
                                    emax
                                                                              d
                                                                                      1 e V
       where,
                      ID = density index (%).
                      emax = maximum attainable void ratio of the sand.
                      emin = minimum attainable void ratio of the sand.
                      e = desirable void ratio in the sample.
                      Pd = dry density of the sample (gr/cm3).
                      Ps = density of the particle of sand = 2.643 gr/cm3.
                      V = volume of the sample (cm3).
                      ms = weight of the sample (gr).

        According to the values of emin and emax given in the table 2, the samples have been
built in order to get three different kinds of densities, which corresponded with the
following values of ID:

                              Loose sample:                     ID = 30 %
                              Medium density sample:            ID = 60 %
                              Dense sample:                     ID = 90 %

        Figure 14 shows the disposition of all the transducers and the connections with the
control panel.


                                                    Load cell                         AIR SUPPLY COMPRESSOR
                                                                                        AIR VACUUM

      LABVIEW                                                                           AIR
      axial force & torque                                                        LABVIEW     Software to receive the data




                                                                  Valve

        Pore pressure


                                                                                                                             Vacuum system
      pore pressure
                                                                                                                              Pressure
                                                                                                                              regulator
       LVDT

      LABVIEW
      axial
      displacement                                                                      Pressure
                                                                                        regulator
           RCDT

      LABVIEW
      rotational
      displacement




                                    Figure 14. Configuration of the HCTA during tests.

                                                                                                                                          34
 New Hollow Cylinder Torsional Apparatus (HCTA)                                    Sergio Valdueza Lozano


           7.1. Repeatability.
        Figure 15 shows all the series of triaxial compression test made with sample of
medium density and 50 KPa of confining pressure. The results demonstrate a good
repeatability, especially in the value of peak force (845.77 N, 804.58 N, 819.37 N and
812.67 N). The value is a bit higher in the test of January 23rd, but even including this
value, the peak force has an average of 820.60 N and a deviator of +/- 17.84 N. According
to the experience of the author, the poor precision of the pressure transducer temporally
used to measure the vacuum (1 KPa) causes this error in repeatability, so it has sense to
agree that the confining pressure used in the test of January 23rd was a bit higher than 50
KPa.



                                     Repeatability (medium density sand)

                                     Jan 23     Jan 24        March 3    March 4

                  900
                  800
                  700
                  600
      Force (N)




                  500
                  400
                  300
                  200
                  100
                   0
                        0      5       10      15        20      25     30         35      40      45
                                                    Displacement (mm)




                            Figure 15. Study of repeatability with compression tests.


         One point where is quite difficult to get the repeatability is at the beginning of the
tests. It is there where the bedding errors have their greater influence (see test of March 3 rd
in figure 15). To solve this problem it is necessary to improve the connection between the
specimen and the loading system. The author suggests using an item with a double keys
system. The first would help to have a high precise approach, narrowing the space between
the holes and the screws until get a rigid contact. The second would help to get a perfect
horizontally, a system like the one used in theodolites.




                                                                                                        35
 New Hollow Cylinder Torsional Apparatus (HCTA)                         Sergio Valdueza Lozano


       7.2. Triaxial compression.
       Figure 16 shows the forces actuating in the test.
The force is applied by means of the pneumatic system
and the pressure by means of applying vacuum inside the
sample. A triaxial compression means that there is no
torque applied to the specimen, as well as that 1 = z and
2 = 3 = r = .

                                                              Figure 16. Triaxial compression.

        The steps of loading for triaxial compression tests are the following. Firstly, all the
pipes in the apparatus and control panel are checked as a matter of security. Only after that
the sample preparation can start (the indications to follow have already been detailed in the
chapter 5). To apply vacuum inside the sample it is not necessary to give much more than
one atmosphere. When the sample is ready, it is time to check the position of all the
transducers, to switch on the computers and to prove that all the informatic system is
working properly, in other words, to verify the data sent by the transducers arrive to the
screen in the computer. After this, the test is conducted at least for two people: one keeps
control of the pressure regulator to increase the force at a slow, but constant, speed; the
second stays in front of the computer checking the displacements received from the
transducers. It is important to say that the apparatus is still in the first phase of
development, so there is not control neither in force or displacement. The person who is in
front of the computer is in charge of noting when the displacements become uncontrolled,
so the sample has achieved the failure; and in charge of giving notice to the person who
takes care of the pressure regulator to stop the test. Finally, all the pressure regulators are
closed and the sample is dismounted carefully. All the peaces are cleaned and got ready for
the next test. The data is extracted from the computer and manipulated to remove possible
evident bedding /tilting errors.

        It has been done eleven triaxial compression tests with three different densities
(loose, medium and dense sand) and two different confining pressures (around 35 and 50
KPa). A summary of the tests is showed in the table 3.

      Triaxial                        3 = 2 = P
                     Density                          F (N)            1 (Kpa)            
   compression tests                     (kPa)
 1      Esy1           L                   50        719,37               193              36,2
 2      Esy2           L                   35        507,75               136              36,0
 3      Esy3           M                   50        845,77               218              38,8
 4      Esy4           M                   32        529,93               137              38,4
 5      Esy5           M                   50        804,58               210              38,0
 6      Esy6           M                   50        817,25               213              38,3
 7      Esy7           M                   35        585,56               151              38,6
 8      Esy8           M                   50        814,08               212              38,2
 9      Esy9           M                   40        665,85               172              38,5
10     Esy10           D                   50        1033,1               256              42,3
11     Esy11           D                   35        712,32               177              42,1

                        Table 3. Main features of triaxial compression tests.

                                                                                             36
 New Hollow Cylinder Torsional Apparatus (HCTA)                         Sergio Valdueza Lozano


        At the beginning of all the tests, the data shows some bedding and/or tilting errors.
This is an identifiable error and, subsequently, easy to extract from the results. However,
sometimes is more difficult to extract them, even when they are identified, and the error is
included in the results (see figure 19 in the chapter 7.2.1.) To minimise it, the connector
between the sample and the loading system should be improved, as it is said in the chapter
7.1.

        Actually, in the triaxial tests it has been used two different ways to make the
connection: one with the screws inside the holes (case 1, picture 12), and other with the
screws outside the holes (case 2, picture 13). Both techniques present different kind of
errors. In the case 1, the error is produced because it does not exist a perfect rigid contact
inside the holes, in other words, the screws make contact with the internal walls of the
holes, transferring to the sample a vertical frictional force, before reaching full contact. In
the case 2, the error is reduced to a lack of horizontality in the sample.




          Picture 12. Case 1, screws                     Picture 13. Case 2, screws
              inside the holes.                              outside the holes.


        As it has been said before, the values of  and b are connected because the inner
and outer pressures are the same. The values of  and b in the axial pure compression test
are the following:

                         arctg  2 z 
                                            

                                   z    
                                            
                                               0        
                                                         z  0    
                                   2
                               2
                                        3
                           b                  0             
                                  
                                   1      3
                                                              2     3




       7.2.1. Results and main features of each test.
               Loose sand. The total weight of sand used to build the specimens was of
       1418 grams. Using the formulation given at the beginning of this chapter, the ID for
       these tests was of 30%, so the samples are of low density. The confined pressure
       was of 50 KPa and 35 KPa, and the data was visualised and recorded every 0,4
       seconds.




                                                                                             37
New Hollow Cylinder Torsional Apparatus (HCTA)                                           Sergio Valdueza Lozano


              The next figures show the results in terms of force-vertical displacement
      and the Mohr-Coulomb circles according to the values showed in the table 3,
      respectively:

                                           Triaxial compression tests (loose sand)

                                                           Esy1    Esy2
                               800
                               700
                               600
                               500
                   Force (N)




                               400
                               300
                               200
                               100
                                 0
                                     0    5     10    15      20      25       30   35      40    45
                                                           Displacement (mm)



                                         Figure 17. Force (N) vs. Displacement (mm).




                                          Figure 18. Angle of friction for loose sand
                                              considering constant cross-area.


              The peak force decreases when the confining pressure is decreased.
      However, both samples have the same angle of friction at failure. Furthermore,
      both tests present the same curve, which is a common smooth curve for soft
      samples and that shows that the sample suffers of a big strain before breaking. The
      fact that the curves are smooth, there are not jumps between consecutive values,
      indicates that the transducers have worked properly and that the apparatus is
      operative. This is going to be a common point in the results of all the tests.



                                                                                                              38
New Hollow Cylinder Torsional Apparatus (HCTA)                     Sergio Valdueza Lozano


             Medium density sand. The total weight of sand used to build the
      specimens was of 1520 and 1515 grams. The ID for these tests was of 61% and
      60%. As it is reflected in the table 3, the confined pressure used was of 32, 35, 40
      and 50 KPa. The data was visualised and recorded every 1 second in Esy3, Esy4
      and Esy5, and every 0,4 seconds in the other tests.

              The next figures show the results in terms of force-vertical displacement
      and the Mohr-Coulomb circles according to the values showed in the table 3,
      respectively:




                              Figure 19. Force (N) vs. Displacement (mm).




                          Figure 20. Angle of friction for medium density sand
                                    considering constant cross-area.


                                                                                        39
New Hollow Cylinder Torsional Apparatus (HCTA)                                         Sergio Valdueza Lozano


              The peak force increases when the confining pressure is increased.
      However, all the samples have the same angle of friction at failure. The falls of the
      curves at the end of each test indicates when the tests were finished and the
      pressure regulators that control the loading were closed. This depends on the time
      the researcher note the sample has arrived to failure, letting pass a bit of time to
      make sure the sample is really broken. The results show that all the tests were shut
      down correctly. Only the test Esy4 maybe was stopped a bit early, but late enough
      to know the peak force.

              Dense sand. The total weight of sand used to build the specimens was of
      1607 grams, and the ID for these tests was of 90%. The confined pressure was of 50
      KPa and 35 KPa, and the data was visualised and recorded every 0,4 seconds. The
      next figures show the results in terms of force-vertical displacement and the Mohr-
      Coulomb circles according to the values showed in the table 3, respectively:

                                             Triaxial compression tests (dense sand)

                                                           Esy10    Esy11
                                 1200

                                 1000
                                 800
                     Force (N)




                                 600
                                 400

                                 200
                                    0
                                        0          10         20         30       40         50
                                                            Displacement (mm)



                                            Figure 21. Force (N) vs. Displacement (mm).




                                             Figure 22. Angle of friction for dense sand
                                                  considering constant cross-area.



                                                                                                            40
 New Hollow Cylinder Torsional Apparatus (HCTA)                               Sergio Valdueza Lozano


               The results for dense samples have identical conclusions to the others for
       loose and medium dense samples: the peak force increases when the confining
       pressure is increased and the samples have the same angle of friction at failure.
       Furthermore, both tests present the same smooth curve with the common
       pronounced force peak, which indicates the sample does not suffer a big strain
       before it breaks, it is just the opposite behaviour of loose samples.

        Figure 23 compare the results in triaxial compression tests with different densities
of sand, but keeping constant the confining pressure (50 Kpa). The results show clearly
two features that change with the density. The first feature is the increase in the force peak
when the density is increased. The second and most important for our analysis is the
change of shape for materials of different density. This different behaviour, from strain
hardening for loose samples to strain softening for dense samples, is a very well known
issue in geomechanics; and the fact that HCTA has been able to identify properly this
feature proves unequivocally the validity of the apparatus.



                                         Triaxial compression tests

                                  Loose sand       Medium dens sand             Dens sand

                          1200
                          1000
                           800
             Force (N)




                           600
                           400
                           200
                              0
                                  0         10         20          30          40           50
                                                    Displacement (mm)


                         Figure 23. Triaxial tests with the same confining pressure (50 Kpa)


        For the similar sand and for relatively low confining pressure (less than 100 KPa)
in triaxial tests, the angles of friction are very similar to the values presented by Lancelot et
al. (1996) and showed in the figure 24. Lancelot et al. (1996) arrives to the conclusion that
the angle of friction decreases softly when the confining pressure is increased. This
behaviour is more accentuated with very low confining pressures, and it tends to disappear
for medium-high confining pressures. Figure 24 shows, for a confining pressure equal to
50 Kpa, that the value of the angle of friction varies between 36º for loose sands and 47º
for dense sands. Without knowing the density indexes related to these two values, it is only
possible to verify that the results for triaxial compression tests are kept inside Lancelot’s
values.

                                                                                                   41
New Hollow Cylinder Torsional Apparatus (HCTA)                                     Sergio Valdueza Lozano




                               55

                               50



                  (degrees )
                               45
                                                                          Hostun dense
                               40
                 j max                                                    Hostun loose
                               35

                               30

                               25
                                    0     20    40    60    80      100
                                        Confining presssure (KPa)




                   Figure 24. Angle of friction vs. confining pressure.
                                (Lancelot et al, 1996)



      7.2.2. Pictures of failure.




            The pictures above show the common torus shape present in all the triaxial
      compression tests.




                                                                                                        42
    New Hollow Cylinder Torsional Apparatus (HCTA)                       Sergio Valdueza Lozano


          7.3. Pure torque.
        Figure 25 shows the forces actuating in the test.
The torque is applied by means of two pneumatic systems
and the pressure by means of applying vacuum inside the
sample. A pure torsional test means that there is axial
force applied to the specimen (P), but there is not deviator
stress (z -  = 0), and that the sample is isotropic
consolidated.

                                                                      Figure 25. Pure torque.

         The steps of loading for pure torque tests are the same than for triaxial compression
tests, so they are explained in the chapter 7.2.

       It has been done four pure torsional tests with the same sand density (medium
density) but the fourth, which sample is of medium-high density; and three different
confining pressures (35, 50 and 80 KPa). It is impossible to know exactly when the
samples broke if there is no control neither in loadings or strains, so the approximation
from torque-rotation to stress-strain has not been done for any test. Therefore, for pure
torque tests the angles of friction and its comparison with the Lancelot’s values are not
given.

          A summary of the tests is showed in the table 4.

      Torque                   2=P
                  Density                  Mt1 (Nm)          3 (kPa)                1 (kPa)
       tests                   (kPa)
1     Esy12          M           50          9,54               5,3                     94,7
2     Esy13          M           35           4,6              13,5                     56,5
3     Esy14          M           50         8,358              10,9                     89,1
4     Esy15          M           80          10,7              29,9                    130,1
                                           Mt2 (Nm)          3 (kPa)                1 (kPa)
                                       1     -8,72             90,8                     9,2
                                       2    -5,909             62,7                     7,3
                                       3     -9,23             93,2                     6,8
                                       4    -14,91            149,8                    10,2

                      Table 4. Summary of the main features of pure torque tests.


        As in the triaxial compression tests, the data shows the bedding of the sample at the
beginning of all the pure torsional tests. As it was mentioned before, this is an identifiable
error and, subsequently, extractable from the results. The improved connector between the
sample and the loading system should minimise this error.




                                                                                               43
New Hollow Cylinder Torsional Apparatus (HCTA)                                                          Sergio Valdueza Lozano


      The values of  and b in the pure torsional tests are the following:


                      arctg  2 
                                                            
                                                          z  
                                                z          O
                              
                                                           
                                                                45                              
                                                                                                z                 r
                                               2
                                         2
                                                    3
                         b                                 0.5                                              3  2 z 
                                                                                                                          
                                               
                                               1      3
                                                                                           1        2       z




      7.3.1. Results and main features of each test.

             Esy12. The total weight of sand used to build the specimen was of 1520
      grams. Using the formulation given at the beginning of this chapter, the ID for this
      test was of 61%, so the sample is of medium density. The confined pressure was of
      50 KPa, and the data was visualised and recorded every 1 second. The torque was
      applied in two directions, completing one cycle and a half.

             Either the data was achieved too slowly or the test was conducted too
      quickly. The error was solved for the next tests getting data every 0.4 seconds and
      applying pressure to the chambers of the two belloframs (in this test it was applied
      pressure only in one of the cylinders), so the torque is applied more slowly.

              The next figure shows the results in terms of torque-rotation:


                                                              1st pure torsional test

                                                                15


                                                                10
                        Torsion (N*m)




                                                                 5


                                                                 0
                                        -30    -20        -10         0      10      20        30       40         50
                                                                 -5


                                                                -10
                                                                      Rotation (degrees)




                      Figure 26. Torque (N*m) vs. Rotation ( º ) for the 1st test.


             Esy13. The total weight of sand used to build the specimen was of 1515
      grams. The ID was of 60%, so the sample is of medium density. The confined
      pressure was of 35 KPa, and the data was visualised and recorded every 0.4 second.
      The torque was applied in two directions, completing four cycles and a half.



                                                                                                                                  44
New Hollow Cylinder Torsional Apparatus (HCTA)                                      Sergio Valdueza Lozano


              The next figure shows the results in terms of torque-rotation:




                                Figure 27. Torque (N*m) vs. Rotation ( º ) for the 2nd test.

             Esy14. The total weight of sand used to build the specimen was of 1515
      grams. The ID was of 60%, so the sample is of medium density. The confined
      pressure was of 50 KPa, and the data was visualised and recorded every 0.4 second.
      The torque was applied in two directions, completing one cycle and a half. The
      torque was applied in two directions, completing two cycles and a half.

              The next figure shows the results in terms of torque-rotation:


                                                   3rd pure torsional test

                                                               15

                                                               10

                                                                5
                 Torque (N*m)




                                                                0
                                -30       -20       -10             0          10   20         30
                                                               -5

                                                              -10

                                                              -15
                                                          Rotation (degrees)



                                Figure 28. Torque (N*m) vs. Rotation ( º ) for the 3rd test.


                                                                                                         45
 New Hollow Cylinder Torsional Apparatus (HCTA)                       Sergio Valdueza Lozano


                Esy15. The total weight of sand used to build the specimen was of 1590
       grams. The ID was of 82%, so the sample is of medium-high density. The confined
       pressure was of 80 KPa, and the data was visualised and recorded every 0.4 second.
       The torque was applied in two directions, completing four cycles and a half. The
       first of them was loaded more or less until sample’s failure, meanwhile in the other
       cycles the specimen was rotated at maximum.

               The next figure shows the results in terms of torque-rotation:




                    Figure 29. Torque (N*m) vs. Rotation ( º ) for the 4th test.

        In all the results it is remarkable that all the cycles are totally repeatable with
exactitude. Another time, like in triaxial compression tests, the curves are smooth without
jumps between consecutive values.

         Comparing the torque peak values of all the results, it is very reasonable that it
increases when the confining pressure increases (as well as the density of the sample in the
last test).




                                                                                           46
New Hollow Cylinder Torsional Apparatus (HCTA)                       Sergio Valdueza Lozano


      7.3.2. Pictures of failure.




              The pictures above show clearly the rupture plane that is common of pure
      torque tests. This plane looks like a shear helicoidal band with an inclination
      between 20º and 25º. This localisation of the rupture is difficult to say where it
      takes place, which varies from one test to other, but it appears mostly in the centre
      of the sample. It is also difficult to confirm or establish a relationship between the
      inclination of the plane and the features of the sample (like density, confining
      pressure or angle of friction).




                                                                                          47
 New Hollow Cylinder Torsional Apparatus (HCTA)                       Sergio Valdueza Lozano



       8. Conclusions.
        With this thesis the author has participated in the final development of the Hollow
Cylinder Torsional Apparatus. This involves to collaborate in the final stage of fabrication
of the HCTA, to design the control panel, to choose and order the pieces missed in the
apparatus or control panel, to install the hardware and software necessary to get and
control the data, to install and calibrate the transducers used to get the experimental data,
etc.

       The Hollow Cylinder Torsional Apparatus (HCTA) of Bristol requires a lot of work
more to reach its completion, but the results obtained until now show that it has good
response in triaxial compression and pure torsion and more than acceptable repeatability,
which demonstrate that the procedure of sample fabrication was good.

        Referencing to the triaxial compression tests, it can be said that the confining
pressure used was good. The results observed in triaxial compression tests are consistent
with the behaviour of the loose, dens and medium sand, even if they are expressed in terms
of force-displacement. It can be observed in the results that the curves force-displacement
show more accentuated peak values with the increase of the densities, and that the curves
are smooth. According to the values obtained for Lancelot et al. (1996) the HCTA can
describe quite well the general behaviour of the sand.

        The aim of the pure torque tests was to know how the system of applying torque
works, because it has never been used before. After improving the method it has been
realised that the confining pressure was very low, since the torque arrived only to 15 Nm
out of 400 Nm. However, highs values of confining pressure were constrained by matters
of security. The transducers worked very well, specially the RCDT, because the cycles
were repeatable, that means there was not sweep in the contact with the RCDT.
Furthermore, the results in torque-rotation show again their consistency when the peak
value of torque increases when the density is increased from low to high density.

        At the end of the tests it is remarkable that the software worked well without bugs
or interruption in the acquisition of data and that the author was enough confident with the
applying of the vacuum.

       In order to gain accuracy in the results, the HCTA has to be improved in different
aspects, especially in the connection between the specimen and the loading system, but
without forgetting the transducers resolution.

        The sample preparation is good to study the general behaviour of the apparatus, but
it is not enough to study the anisotropy in the sand, of its behaviour for small strains. A
pluviation method would improve quite well the uniformity in the sample.

       The author makes some suggestions for future research and development:

          Installation of the water net.
          Control of internal displacements.
          More tests in drain and undrained conditions.
          More tests controlling independently the parameters b and .


                                                                                           48
New Hollow Cylinder Torsional Apparatus (HCTA)                    Sergio Valdueza Lozano




      Finally, the author has achieved some good skills in experimental works:

         Able to make some further works with a Hollow Cylinder Torsional Apparatus
      or with other soil mechanic devices.

         Know how to apply forces and torques in a laboratory work and how to obtain
      data.

         Follow the procedure to work safely with high pressure and electrical
      equipment.

         Be able to identify the weaknesses of a sample preparation and make some
      suggestions to reach a good standard.




                                                                                       49
New Hollow Cylinder Torsional Apparatus (HCTA)                       Sergio Valdueza Lozano




    9. Acknowledgements.

     I would like to express my thanks to Dr. Erdin Ibraim (University of Bristol) for
  supervising and helping me in conducting this report and for his invaluable support
  every time I needed it.

      I also want to thank all the technicians of the University of Bristol for their entire
  dedication and efficiency to this project; it would never have finished on time without
  their collaboration.

     Finally, I want to thank Dr. Eduardo Alonso (Universidad Politècnica de
  Catalunya) for his support from Barcelona and for helping me in the elaboration of this
  report.




                                                                                          50
New Hollow Cylinder Torsional Apparatus (HCTA)                    Sergio Valdueza Lozano



    10. References.
      Bishop, A. W. and Henkel, D. J. (1962). The measurement of soil properties in
  the triaxial test. (2nd edition) London: Arnold.

      Bjerrum, L. (1973). Problems of soil mechanics and construction on soft clays and
  structurally unstable soils. Proc. VIIth Int. Conf. on Soil Mechanics and Foundation
  Engineering, Moscow, Vol 3, 111-159.

      Broms, B. B. and Casbarian, A. O. (1965). Effects of rotation of the principal
  stress axes and the intermediate stress on shear strength. Proceedings of the 6th
  International Conference on Soil Mechanics and Foundations Engineering. Montreal.
  Vol. 1, pp. 179-183.

      Cooling, L. F. and Smith, D. B. (1936). The shearing resistance of soils. Journal
  of the Institution of Civil Engineers. Vol. 3, pp. 333-343.

     Hardin, B.O. and Drnevich, V.P. (1972). Shear modulus and damping in soils:
  measurement and parameter effects. Journal of the Soil Mechanics and Foundations
  Engineering. Proceedings of the American Society of Civil Engineers. Vol. 98, No.
  SM6, pp. 603-624.

      Hight, D. W., Gens, A. and Symes, M. J. (1983). The development of a new
  hollow cylinder apparatus for investigating the effects of principal stress rotation in
  soils. Geotechnique. Vol. 33, No. 4, pp. 355-383.

      Hight, D. W., Gens, A. and Symes, M. J. (1985). Undrained anisotropy and
  principal stress rotation in saturated sand. Geotechnique. Vol. 34, No. 1, pp 11-27.

     Hou, E., Negussey, D., Sayao, A. and Vaid, Y. P. (1990). Generalised stress-
  path-dependent soil behaviour with a new hollow cylinder torsional apparatus.
  Canadian Geotechnical Journal, N° 27, pp 601-616.

     Ishibashi, I. and Sherif, M.A. (1974). Soil liquefaction by torsional simple shear
  device. Journal of the Geotechnical Engineering Division. Proceeding of the American
  Society of Civil Engineers. Vol. 100, No. GT8, pp. 871-887.

      Ishibashi, I., Jenkins, J.T., Choi, J.W. and Parker IV, C.L. (1996). The
  influence of boundaries on the volumetric behaviour of solid and hollow cylindrical
  specimens of glass beads. Soils and Foundations. Japanese Geotechnical Society. Vol.
  36, No. 2, pp. 45-55.

     Ishibashi, I., Kawamura, M. and Bhatia, S. K. (1985). Torsional simple shear
  apparatus for drained and undrained cyclic testing. Proc. of ASCE Annual convention,
  Session on Advances in the Art of Testing Soils Under Cyclic Conditions, pp. 51-73.

     Lade, P.V. (1975). Torsion shear tests on cohesionless soil. Proceedings of the 5th
  Pan-American Conference on Soil Mechanics and Foundations Engineering. Buenos
  Aires. Vol. 1, pp. 117-127.


                                                                                       51
New Hollow Cylinder Torsional Apparatus (HCTA)                      Sergio Valdueza Lozano


     Lancelot, L., Al Mahmoud, M. and Shahrour, I. (1996). Comportement du sable
  d'Hostun sous faibles contraintes. Revue Française de Géotechnique, N° 74, pp 63-75.

     Lomise, G.M., Kryzhanovsky, A.L., Vorontsow, E.I. and Goldin, A.L. (1969).
  Study of deformation and strength of soils under three-dimensional state of stress.
  Proceedings of the 7th International Conference on Soil Mechanics and Foundations
  Engineering. Mexico. Vol. 1, pp. 257-265.

     Karchafi, M. (1988). Contribution a l’etude du comportement des materiaux
  granulaires sous solicitations rotationelles. These de doctorat. Ecole Centrale de Paris.

     Miura, K., Miura, S. and Toki, S. (1986). Deformation behaviour of anisotropic
  dense sand under principal stress axes rotation. Soils and Foundations. Japanese
  Society of Soil Mechanics and Foundations Engineering. Vol. 26, No. 1, pp. 36-52.

     Miura, K., Toki, S. and Miura, S. (1986). Deformation prediction for anisotropic
  sand during the rotation of principal stress axes. Soils and Foundations. Japanese
  Society of Soil Mechanics and Foundations Engineering. Vol. 26, No. 3, pp. 42-56.

     Muramatsu, M. and Tatsuoka, F. (1981). Cyclic undrained stress-strain
  behaviour of dense sand by torsional simple shear test. Bulletin of Earthquake
  Resistant Structure Research Centre 14, March, 79-101.

     Nakata, Y., Hyodo, M., Murata, H. and Yasufuku, N. (1998). Flow deformation
  of sands subjected to principal stress rotation. Soils and Foundations. Japanese
  Geotechnical Society. Vol. 38, No. 2, pp. 115-128.

     Palomero, J. (2002) New hollow cylinder torsional apparatus. Major Project
  Report. Department of Civil Engineering. University of Bristol.

      Saada, A.S. and Baah, A.K. (1967). Deformation and failure of a cross-
  anisotropic clay under combined stresses. Proceedings of the 3rd Pan-American
  Conference on Soil Mechanics and Foundations Engineering. Caracas. Vol. 1, pp. 67-
  88.

     Saada, A.S. (1968). A pneumatic computer for testing cross anisotropic materials.
  Materials Research and Standards 8, No. 1, 17-23.

      Saada, A.S. and Zamani, K.K. (1969). The mechanical behaviour of cross-
  anisotropic materials. Proceedings of the 7th International Conference on Soil
  Mechanics and Foundations Engineering. Mexico. Vol. 1, pp. 766-795.

      Saada, A. S. (1988) Hollow Cylinder Torsional Devices: their advantages and
  limitations. Advanced Triaxial Testing of Soil and Rock, American Society for Testing
  and Materials, Philadelphia, pp 766-795.

     Sayao, A. and Vaid, Y. P. (1991). A critical assessment of stress non-uniformities
  in hollow cylinder test specimen. Soils and Foundations. Japanese Society of Soil
  Mechanics and Foundations Engineering. Vol. 31, No. 1, pp 60-72.



                                                                                         52
New Hollow Cylinder Torsional Apparatus (HCTA)                    Sergio Valdueza Lozano


      Symes, M.J., Gens, A. and Hight, D.W. (1984). Undrained anisotropy and
  principal stress rotations in saturated sand. Geotechnique. Vol. 34, No. 1, pp.11-27.

      Tatsuoka, F., Muramatsu, M. and Sasaki, T. (1982). Cyclic undrained stress-
  strain behaviour of dense sands by torsional simple shear test. Soils and Foundations.
  Japanese Society of Soil Mechanics and Foundations Engineering. Vol. 22, No. 2, pp.
  55-70.
      Tatsuoka, F., Sonoda, S., Katsushige, H., Fukushima, S. and Pradhan, T.B.S.
  (1982). Failure and deformation of sand in torsional shear. Soils and Foundations.
  Japanese Society of Soil Mechanics and Foundations Engineering. Vol. 26, No. 4, pp.
  79-97.

      Vaid, Y. P. and Sivathayalan, S. (2002). Influence of generalised initial state and
  principal stress rotation on the undrained response of sands. Canadian Geotechnical
  Journal, N° 39, pp 63-76.

      Yoshimi, Y. And Oh-Oka, H. (1973). A ring torsion apparatus for simple shear
  test. Proceedings of the 8th International Conference on Soil Mechanics and
  Foundations Engineering. Moscow. Vol.1, Tome 1, pp. 501-506.

      Yoshimine, M., Ishihara, K. and Vargas, W. (1998). Effects of principal stress
  direction and intermediate principal stress on undrained shear behaviour of sand.
  Soils and Foundations. Japanese Geotechnical Society. Vol. 38, No. 3, pp. 179-188.

      Zdravkovic, L. and Jardine, R.J. (1997). Some anistropic stiffness characteristics
  of a silt under general stress conditions. Geotechnique. Vol. 47, No. 3, pp. 407-437.

      Zdravkovic, L. and Jardine, R.J. (2001). The effects on anisotropy of rotating the
  principal stress axes during consolidation. Geotechnique. Vol. 51, No. 1, pp. 69-83.




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