A New Computer Controlled Hollow Cylinder Torsional Shear Apparatus Un nouvel appareil d’essai de cisaillement torsionel sur cylindre creux João P. Bilé Serra Laboratório Nacional de Engenharia Civil, Portugal; [email protected] Patrick Hooker GDS Instruments Ltd, United Kingdom KEYWORDS: Hollow Cylinder, Torsional shear, Cyclic test, Test apparatus, Computer control, Sand. ABSTRACT: A new hollow cylinder torsional shear apparatus, the GDS HCA, is introduced. It is a fully computer automated closed-loop feedback system which provides accurate control of the loads, displacement, rotation, calculated stresses and strains. It allows the performance of monotonic, slow cyclic and dynamic tests on soil specimens in the laboratory. In order to illustrate the apparatus capabilities some results of a cyclic shear test on a dense sandy sample are presented. RESUME: Un nouvel appareil d’essai de cisaillement torsionel sur cylindre creux, le GDS-HCA a été développé. Il s’agit d’un système servo-contrôlé par logiciel qui permet de contrôler les forces, le déplacement, la rotation et, parmi les variables calculées, les contraintes et les déformations. Des essais monotones, cycliques lents et dynamiques peuvent être réalisés avec cet appareil. Un essai de cisaillement cyclique effectué sur un échantillon de sable dense illustre l’usage de l'appareil.

1

INTRODUCTION

It is a matter of fact that test devices and test methods are not currently available to satisfy the broad range of requirements related to those situations of interest in geotechnics which may produce shear strains varying by more than five orders of magnitude. Torsional shear testing devices have become the devices of choice to study the monotonic and cyclic behaviour of soils especially when used with a hollow cylinder specimen. The arguments for hollow cylinder specimens torsional testing include (Saada, 1988): minimal effects of end platens, ease of testing with anisotropic stress conditions, and complete definition of the state of stress, which can be accurately measured. As a consequence, in recent years, increasing attention has been given to the laboratory testing of soils in torsional shear, particularly with regard to cyclic behaviour. Given the recognized limitations of the cyclic triaxial test, the benefits of torsional shear testing make it clear that performing tests with torsional shear devices has much to offer the practice of geotechnical engineering and soil mechanics. References to the existence of hollow cylinder torsional devices go back as far as 1965, (Broms and Casbarian, 1965). After that landmark a long list of hollow cylinder torsional apparatuses have been described, the most recent references are: (Hight et al., 1983), (Alarcon et al., 1986), (Ampadu and Tatsuoka, 1993), (Huang et al. 1994). A new hollow cylinder torsional shear apparatus, the GDS HCA, is introduced here. It is a fully automated system combining advanced triaxial testing features with advanced torsional shear capabilities. A computer-automated closed-loop feedback system provides accurate and independent control of the load, torque, vertical displacement, rotations, pressures and calculated stresses and strains.

Anisotropy in granular materials is caused either by the arrangement of particles, such as occur in natural deposits in which the grains may have their major axis on the bedding plane, or by spatial distribution of contacts and contact forces. Further to this so-called inherent anisotropy (Arthur and Menzies, 1972) induced anisotropy is caused in the specimen by the non-reversible strain increments during the follow up of stress path. Only through carefully designed and controlled tests is it possible to clarify the influence of the stress path followed by the soil on the strength and deformability. The importance of experimental studies is further emphasized by the path dependence of strain behaviour. With the GDS HCA fully automated control of generalized total stress path, i.e. in the (p, q, b, α) stress space, is made possible. Several imposed strain path tests such as the simple shear test and the plane strain test may also be carried out in this apparatus. In addition to the tests on hollow cylindrical test specimen described above the system can also be used for carrying out advanced triaxial compression and extension tests. These triaxial tests can be executed under stress or strain control with independent control of the axial and torsional modes of operation. The use of this apparatus is illustrated by a stress controlled undrained torsional shear test of a sand specimen. The specimen was prepared using a new automatic sand pluviator (Bilé Serra, 1999). During the test four stress cycles of low amplitude were followed by four extra cycles of medium amplitude thus enabling two distinct patterns of stress-strain behaviour to be observed: the first is in the small strain domain with no pore pressure build-up and the second occurs in the medium amplitude range in which the joint effect of dilatancy and compaction tendency causes the pore pressure to increase with an oscillatory pattern and the shear strain amplitude to rise. 2

TORSIONAL SHEAR TESTS

In a torsional shear apparatus the combination of axial and torsional loadings leads to principal stresses that are inclined on the axes of symmetry of the material. The use of different inner (inside the hollow cylinder test specimen) and outer pressures causes a general average state of effective stress described by the following effective stress tensor:

 σ 'r  σ' =  0 0 

0 σ 'θ τz θ

0   τθz  σ 'z 

(1)

Each component in this tensor represents the average value over the sample volume of the corresponding stress field. While σ 'θ and σ 'z are deduced based on equilibrium conditions, the definition of the remaining components depends on the basic assumptions about the stress field. In the present paper the definitions as in (Hight et al., 1983) were used. The ability to control each of the components is only possible by independent advanced control over the axial force, torque, inner and outer pressures. These features are available in the present apparatus thus making possible generalized stress path testing. The assumed average strain tensor is given by

ε r ε = 0   0

0 εθ εz θ

0  εθ z   εz 

where the strain components are those proposed in (Hight et al., 1983). On the one hand, controlling the axial strain ε z and the off-diagonal component ε zθ may be straightforward, since they are, respectively, expressed as a direct function of the axial displacement and of the torsional rotation, respectively. On the other hand, advanced strain path testing (e.g. plane strain testing mode) requires very precise servo-control of the confining pressures.

3

DESCRIPTION OF HCA

The HCA consists of a combined cell and actuator. A schematic drawing of the HCA is shown in Figure 1.

C

A

B

D

E

F

L G

H

K

I J

Figure 1 – Schematic drawing showing layout of Hollow Cylinder Apparatus.

The cell, containing the test specimen and the confining fluid, is designed to be very strong, both axially and rotationally. This strength is achieved by the use of three large section tie rods (A) between the cell top and the cell base. These tie rods are rectangular with the longest side facing the test specimen. This arrangement ensures high stiffness to torque. The cell chamber (B) is made from a transparent plastic material and is rated at 1700 kPa. A submersible load/torque cell (C) is attached rigidly to the cell top. The load/torque cell can be easily changed – two sizes are routinely used with the system, 100Nm/10kN and 30Nm/3kN. A counterweighted lifting system (not shown) is used to allow the cell top to be raised, lowered and balanced in any intermediate position as an aid to test specimen set-up. Exchangeable base platens can be attached to the ram (L) to allow for two sizes of test specimen (100 outer diameter/60 inner diameter (100/60) and 70/30). The ram (L) passes into the cell chamber via the balanced ram chamber (F) and the cell base. The balanced ram is designed to ensure that there is no disturbance to confining pressure under dynamic axial loading conditions. This is achieved by ensuring that when the ram enters the cell a matching volume of water leaves the cell and enters the balanced ram chamber. An associated effect is that changes in cell pressure cause a zero resultant force on the ram (L). Axial load and displacement is generated by a high power brush less dc servomotor (K) attached to the base of the ball screw (J) by means of a high stiffness, zero backlash toothed belt drive. Rotation

of the ball screw (J) causes the ball nut (I) to move axially, this motion is transferred to axial motion in the ram (L). The ball nut (I) is prevented from rotating by means of a linear guide (not shown). Rotational motion is added to the axial motion by means of the splined shaft (G). A second brushless dc servomotor (H) is attached to the splined shaft (G) by means of a high stiffness, zero backlash toothed belt drive and is used to generate torque or displacement as required. Control of load/displacement and torque/rotation is provided by specially designed high-speed data-acquisition and control (HSDAC) cards. These cards are resident on the pc ISA bus and provide facilities for both static and dynamic control of load/displacement and torque/rotation. Feedback for load/torque is derived from the combined load/torque cell and feedback for displacement/rotation is derived from high resolution rotational encoders attached to the motors (H & K). The HSDAC cards can select either the load/torque channel or the displacement/rotation channel as the current parameter to be controlled. Facilities exist in the HSDAC card to seek to a target or to follow a previously downloaded repetitive waveform (normally sinusoidal). The HSDAC cards have the capability to control accurately from dc to 10 Hz. Putting this power into the pc resident cards means that the program running in the pc has relatively little to do and therefore the power of the pc is largely irrelevant to the speed of operation of the system. For quasi-static tests the control program running in the pc calculates required targets and passes these targets to the HSDAC cards to carry out the control procedures. There are three pressures to control in the hollow cylindrical test specimen, these are: outer pressure, inner pressure and the back pressure. These pressures are controlled by three GDS advanced pressure/volume controllers of 2 MPa/200 cc capacity. If it is necessary to maintain low pressure differences between the inner and outer pressures or between the outer pressure and the back pressure, then advantage is taken of the ability of the pressure controllers to control via a second transducer – in this case low range wet/wet differential pressure transducers. The back pressure controller is used to measure volume change in the test specimen and the inner pressure controller is used to measure volume changes in the inner space of the hollow cylinder test specimen. The ability to accurately control these pressures and volume changes is vital for carrying out specialised low speed tests such as stress paths in the (p,q,b,α) stress space or simple shear. The HSDAC cards are used for data acquisition at both high and low speeds. Each card is capable of acquiring data from up to eight channels. The parameters normally acquired are as follows: (i) Axial load, (ii) Axial deformation; (iii) Torque, (iv) Rotation, (v) Local external axial strain during triaxial tests (two channels), (vi) Local external radial strain during triaxial tests, (vii) Pore pressure (two channels), (viii) Inner pressure, (ix) Outer pressure, (x) Back pressure, (xi) Inner volume change, (xii) Specimen volume change, (xiii) Small strain external displacement, (xiv) Small strain external rotation. The local external axial and radial strain devices are Hall Effect local strain transducers (Clayton and Katrush,1986). Pore pressure can be measured using an external pore pressure transducer connected to the base pedestal, additionally provision is made for the measurement of pore pressure using a mid-plane pressure transducer that is attached directly to the test specimen at its mid height. Inner pressure, outer pressure and back pressure are measured using the output of the GDS digital pressure/volume controllers. In addition inner, outer and back pressures are measured using separate transducers attached to the cell to enable dynamic as well as static measurements to be made. Volume changes are measured using the output of the GDS pressure/volume controllers. In order to ensure that the compliance of the motor drive system can be estimated high quality LVDTs have been used to measure axial displacement and rotation directly on the load ram. These LVDTs are designed specifically for small strain measurements. The use of intelligent parameter controllers (not in the pc) means that very complex control procedures (e.g. stress paths in (p,q,b,α) stress space) can be routinely carried out. The full range of tests that the machine is capable of performing are described below.

4

CONTROL CAPABILITIES FOR HCA

The following Table shows those parameters that can be independently controlled; this means that a hardware based controller exists to directly control that parameter, to match a target sent by the computer, without the computer being involved in the control process. There are five independent axes of control. Where more than one parameter is assigned to an axis this means that only one item in the list can be controlled at any one time, for example either torque can be controlled or rotation can be controlled but both cannot be controlled independently at the same time. Table 1.Independent axes of control. Axis 1 2 Static variable Kinematical variable

3

4

5

Axial force

Torque

Outer pressure

Inner pressure

Back pressure

Axial displacement

Rotation

Outer volume change

Inner volume change

Specimen volume change

All of the above parameters can be controlled in quasi-static tests. In dynamic tests at frequencies up to 5 Hz only parameters one and two can be controlled. The requirement for dynamic control over outer pressure, inner pressure and back pressure is not necessary because for a typical dynamic test the test specimen is undrained, the outer pressure is equalised with the inner pressure and the dynamic balanced ram ensures that the outer pressure is not disturbed by motion of the loading ram. If the computer is used to execute some control algorithm it is possible to carry out more complex control for quasi-static tests. Options exist to control the derived parameters for hollow cylinder test specimens listed in Table 2. Table 2. Derived control parameters. Axis 1 2 Variable

σz

τ zθ

3

4

3,4

Constant outer diameter

Constant inner diameter

Constant wall thickness

Generalised HCA control is achieved by allowing the control path for each axis to be independently selected according to some time based reference. The control paths offered are: (i) Constant value, (ii) Ramped value (from a start value to and end value), (iii) Cycled value (sine, square or triangle). This ability for HCA generalised control allows the user to perform a range of tests from simple to very complex. Simple tests could be modulus tests (Young’s or shear) performed by keeping the inner pressure and outer pressure constant and ramping or cycling either deformation or rotation. Examples of more complex tests could be cycled σ z or τ zθ , constant σ z with cycled outer pressure or back pressure, and simple plane strain tests. The degree of control means that complex tests like simple shear can be routinely carried out in a number of ways. For example, by specifying constant wall thickness the simple shear requirement is established, it is then possible to add to this other control parameters such as cycling rotation, torque or σ z . The full control capabilities of the new HCA are mobilized in the implementation of the generalised stress path capability. The hardware design and ease of control means that it is relatively straightforward to implement complex control algorithms. The stress path control capability allows a number of linear paths to be defined in terms of the controlled parameters p,q,b,α. Each linear path is defined in terms of its end-points in the (p,q,b,α) stress space. Any number of paths can be executed sequentially thus allowing complex geotechnical processes to be modeled. The degree of control and ease of control provided by this new piece of apparatus means that one can carry out tests previously requiring many different systems. The system can be used to replace triaxial systems (static and dynamic), true triaxial systems, simple shear systems and of course it is a complete hollow cylinder apparatus for both static and dynamic work.

5

TORSIONAL SHEAR TEST OF PLUVIATED SAND SPECIMEN

To demonstrate the capabilities of the new apparatus, a set of cyclic torsional shear tests were performed (Bilé Serra, 1998) on Rio Maior sand (specific gravity = 2.65, maximum void ratio = 0.889, minimum void ratio = 0.516). The results of one of such tests are presented herein. The dense sample (outer diameter =70 mm, inner diameter = 30 mm, height = 140 mm) was prepared at a relative density of 77% by means of a sand-pluviator specifically devoted to the set-up of homogeneous hollow cylinder samples (Bilé Serra, 1998). The sand grains are rained in a dry state from a three column-mounted container and passed through three ASTM sieves in order to achieve uniform flow in the air. Given the influence that both the height of fall and the rate of pluviation at the specimen surface have in the local density of the solid skeleton care was taken to keep both of the parameters approximately constant during pluviation. The hollow cylinder space is created by two specially designed formers: an interior collapsible two part inner former with a membrane in place and a four part collapsible former with an outer membrane permanently sustained under vacuum during pluviation. This assembly is positioned on a movable base axially aligned with the sieves under the rectangular container. During pluviation the base is moved downward at a constant speed (equal to the speed of heightening of the sample surface) so as to keep the effective falling height constant. The specimen was consolidated under an isotropic effective pressure of 200 kPa and a back pressure of 245 kPa. The test was conducted under shear stress control with axial stress and both outer and inner confining pressures constant and with no drainage allowed. A total of eight sinusoidal cycles were applied. Figure 2 depicts the shear-stress/shear-strain hysteresis loops. During the first four cycles a shear stress amplitude of 35 kPa was applied. 100

τzθ (kPa)

50

0

-50

-100

γzθ

-3.E-03 -2.E-03 -1.E-03 0.E+00 1.E-03 2.E-03 3.E-03

Figure 2 - Shear stress – shear strain hysteresis loops.

There was a steady pore pressure build-up to the final value of 10 kPa at the end of the four initial cycles (cf. Figure 3). During each of the subsequent cycles the pore pressure variation was influenced both by the densifying tendency of the sample and by dilatancy, showing an oscillatory pattern. At the end of each cycle the net pore pressure build-up reflected the importance of the densifying process between two successive cycles. In Figure 4 the inherent cross anisotropy of the sample caused by the gravity pluviation is evident from the ratio between the axial shear strain and both horizontal shear strains. 6

CONCLUSION

A new hollow cylinder apparatus has been described. This new equipment has been designed to give an extensive range of element testing capabilities. The equipment can perform both quasi-static and dynamic tests with sinusoidal waveforms up to 5Hz at both small and large strains. The hardware

implementation has been designed to remove computing load from the host computer and thus simplify the control software. The supporting applications software is designed to give the user flexibility in the use of the equipment with both hollow cylinder and solid cylinder (triaxial) tests supported. The combination of intelligent hardware, comprehensive systems software and flexible applications software means that even highly complex procedures, such as stress paths defined in (p,q,b,α) stress space, can be routinely carried out. The equipment represents the ultimate single piece of advanced laboratory soil testing equipment capable of carrying out tests normally requiring many separate testing systems – advanced triaxial, true triaxial, shear box, and simple shear apparatus. σr (kPa)

200

200

σθ (kPa)

100

100

t (min)

0 0

0

100

σz(kPa)

200

t (min)

0

100

τzθ (kPa)

100

50

0

100

-50 t (min)

0 0

0

100

p (kPa)

200

t (min)

-100

100

∆u (kPa)

100 90 80 70 60 50

100

40 30 20 t (min)

0 0

100

10

t (min)

0 0

100

Figure 3 - Variation of effective stress tensor components, mean effective pressure and pore pressure buildup.

εr

εθ

2.E-04

2.E-04

1.E-04

1.E-04

0.E+00

0.E+00

t (min)

-1.E-04 0

t (min)

-1.E-04

100

0

100 γzθ

εz 3.E-03

1.E-04

2.E-03 0.E+00 1.E-03 0.E+00

-1.E-04

-1.E-03 -2.E-04 -2.E-03 t (min)

-3.E-04 0

100

t (min)

-3.E-03 0

100

Figure 4 - Variation of strain tensor components.

REFERENCES Ampadu, S. K. and Tatsuoka, F. (1993). A Hollow Cylinder Torsional Simple Shear Apparatus Capable of a Wide Range of Shear Strain Measurement, Geotechnical Testing Journal, GTJODJ, Vol. 16, No. 1, March, 3-17. Arthur, J.R.F. and Menzies, B.K. (1972). Inherent anisotropy in a sand. Geotechnique Vol.22, No. 1, 115-128. Bilé Serra, J.(1998). Numerical Modelling and Experimental Characterization of Cyclic Behaviour of Non-cohesive Soils. Applications to Earthquake Engineering, Dr. Eng. Thesis, Instituto Superior Técnico, Universidade Técnica de Lisboa (in Portuguese). Broms, B. B. and Casbarian, A. O. (1965). In Proceedings, Sixth International Conference on Soil Mechanics and Foundation Engineering , Montreal, Vol. 1, 179-183. Clayton, C. R. I. and Katrush, S. A. (1986). A new device for measuring local axial strains on triaxial specimens, Geotechnique Vol. 36, No. 4, 593-597. Huang A., Hsu, S. , Kuhn, H.(1994). A Multiple Purpose Soil Testing Apparatus, Geotechnical Testing Journal, GTJODJ, Vol. 17, No. 2, June, 227-232. Saada, A. S. (1988). Hollow Cylinder Torsional Devices: Their Advantage and Limitations, Advanced Triaxial Testing of Soil and Rock, ASTM STP 977, R. Donaghe, R. Chaney, M. Silver, Eds., American Society for Testing Materials, Philadelphia, 766-795.