3.8 EXPERIMENTAL PROGRAMME AND TEST PROCEDURE

The main objectives o f this series o f tests were for familiarisation with the underlying operational principal o f the DSC, and for verifying the results with others who used the DSC. These were achieved by comparing results with those o f Wong, 1986 and Dalili, 1991 .

The preliminary test programme was a series o f tests similar to that done by previous researchers (eg: Wong, 1986 and Dallili, 1991) in which monotonie shear tests were performed on both dense and loose sand samples with the minor principal stress kept at 14 Kpa. All the sand samples were sheared in a dry and drained state with the pore air pressure at atmospheric pressure. The testing procedures for both dense and loose sand were identical to the other workers.

3.8.1- Constant Direction Monotonie Shear Tests

Constant direction monotonie shear tests are those in which each principal stresses is maintained in a constant direction through a test. Figure 3.15.C shows the stress path for this series o f tests. It can be seen that the stress path does not give any information on the directions o f the principal stresses. The direction o f the major principal stress (i|/) is defined in Figure 3.15.b.

All the samples were prepared such that the direction o f sand deposition was normal to the subsequent plane o f strain which also eliminates any influence o f inherent anisotropy in the plane o f strain.

This series o f tests with a range o f major principal stress direction (v|/) between 0° & 90^ were run on both dense and loose sand specimens. The only differences in this series were that even though all samples should undergo the same stress path the normal and shear stress applied at the sample boundaries will differ. There should be no differences to the principal stress and strain data and the results should produce a unique stress-strain relationship together with uniform strain distribution throughout the samples. Deviation from this uniqueness could be due to improper operational procedures, application o f non-uniform or wrong boundary normal and shear stresses, boundary restraints, or imprecise measurements o f the applied stresses and associated strains. Therefore the evaluation process involved the comparison o f stress-strain relationships from tests at various v|/ angles, analysis o f strain distributions within the samples, and the coincidence o f the major principal stress and strain increment directions.

The plane strain tests during the shearing stage followed a stress path (Figure 3.15.c) similar to that described by Wong (1986) and Dalili (1991) in which [b= (cj2-cj3)/(ai- (Tg)] was maintained at 0.3.

3.8.2- General Procedures For DSC Testing

Once a sand sample had been positioned and centred in the DSC using the methods explained in Section 3.4, an isotropic stress was applied to the faces o f the sample

while it was under negative pressure. The magnitude o f this isotropic stress was equal to the value o f the minor principal stress o f the chosen stress path, ie. 14kpa. Application o f negative pore pressure at 14kpa to the sample during the initial setting up procedure was unavoidable and necessary, to transfer the sample to the apparatus without disturbance.

Prior to releasing the negative pressure an inspection was made to ensure that every aspect o f setting up was correct. The sample was centred, the shear sheets were properly aligned, the yokes were in contact with the piston rods, the retaining vanes were in the right position, the correct regulators were in operation and the main compressor was on. Negative pressure was then released.

At this stage a radiograph o f the sample was taken, developed and fixed. Once the quality o f the radiograph was acceptable. This radiograph was the reference film from which the subsequently induced sample strains were computed. The stress ratio was slowly increased by small adjustments o f the pressure regulators that apply normal and shear stresses and to keep a constant minor principal stress direction and magnitude. All intermediate radiographs were taken at suitable stages until the sample reached failure.

Ideally normal and shear stress increments should always be applied simultaneously to the sample to maintain a constant major principal stress direction. The simultaneous application o f the boundary stress was impossible. Therefore stress increments were increased in a sequential series o f the smallest convenient increments by always starting with the normal stresses being increased before the shear stresses. The small

path and major principal stress direction. Obviously, this technique led to many mini­ increments before the strain increment was big enough to warrant a radiograph.

As the sample strained under increasing boundary stresses, the sample changed shape and the boundary stresses no longer acted on orthogonal surfaces, particularly when shearing o f loose samples where large deformations occurred. The corrections (Rodriguz, 1977) are defined in Figure 3.16 and the boundary stresses could be computed from the following equations and corrections made increment by increment according to the current measurements o f the deformed shape.

C7a=l/2a3 [ (R+1) + ( R- 1) c o s 2 (v^-ai ) ]

Gb=l/2(73 [ (R+1) + ( R- 1) c o s 2 (V|/-pi) ]

Ta=l/2(73 (R-1) s i n 2 (v|/-ai)

Tj3=l/2a3 (R-1) s i n 2 (ijz-Pi)

where the a^and pi were the angles o f distortions which could be measured using a protractor through the glass window o f the top platen between each radiograph.

In order to prevent instability o f the sample in the DSC, the sample faces should remain parallel to the backing plates and shear sheets at all stages o f deformation. Thus, adjustment o f backing plates and alignment o f shear sheets was carried out when necessary. Again adjustment o f backing plates and alignment o f shear sheets should be continuous as the test proceeds. This is possible only if the shear sheets and normal pressure bags are adjusted automatically. Here these adjustments were performed by hand for shear sheets and by using adjusting screws for backing plates.

The alignments were particularly important in tests where \|/=45° as the sample changed shape from a square to a rhombus.

When testing dense sand, where sudden failure could occur, the apparatus may become unstable and a rapid manual response was needed to avoid damage to the more delicate parts o f the apparatus. The sample was again subjected to a negative pressure and the main air supply valve was switched off. This allowed all pressurised and stretched components to relax together whilst the sample remained intact.

3.8.3- Stress And Strain relationship

The stress-strain responses o f both dense and loose sand samples, are shovm in figures 3.17, 3.18 respectively. They are presented on a principal stress ratio (cr/oTj) vs. major principal strain graphs whilst in which the major principal strains are plotted against minor principal strains.

As it can be seen from Figures 3.17 and 3.18 , that for both dense and loose sand specimens, during different constant direction monotonie shear tests, the results were very close and a single curve could quit well describe the behaviour. This indicated that, the stress strain curve could be achieved irrespective o f the difference o f the applied major principal stress direction and proved the apparatus.

Tests on dense samples (Figure 3.17), were terminated as soon as a rupture layer developed. This usually occurred at approximately a major principal strain o f 3.5% and corresponded to a stress ratio o f 7 ± 0.2. The actual stress ratio to cause rapture was not precise. It is thought that at about a stress ratio o f 7 a rupture layer can be

when the adjustment o f normal pressure bags, backing plates and the alignment o f the shear sheets are being conducted reaching to this stress ratio. For instance, too much adjustment o f the backing plates may induce boundary disturbance and trigger the rupture layer at lower stress ratios and also lack o f alignment o f shear sheets may result in a thrust back into the sample and delay the formation o f failure planes. The angle o f shearing resistance, 48.5° (i.e.sin (j)f=(R-l)/(R+l)), associated with the stress ratio o f R=7.0 is comparable with that for heighten Buzzard sand at the same voids ratio tested at C73=14kpa under plane strain conditions by other workers, 49° with DSC ( Wong, 1986), 48° with the Biaxial tester (Ogunbekun, 1988) and 48.5° with the DSC (Dalili, 1991).

Figure 3.18 presents the results o f loose sand tests where no rupture planes were observed. For the loose samples, the tests were terminated when a small increment o f stress resulted in large deformation, and this state o f stress was interpreted as failure. This occurred at a major principal strain of about 11%. The associated stress ratio o f approximately 4.1, and the corresponding angle o f friction (|)f o f 37.5° is comparable to the values o f 39.5° obtained by Rodriguez (1977) and Wong (1986), 38° by Dalili (1991) using the DSC and 39° with the Biaxial tester (Ogunbekun, 1988) for sand o f the same voids ratio and at same stress level o f a3=14Kpa.

The strain behaviour o f the dense and loose samples are also illustrated in Figures 3.17 and 3.18 respectively. An average relationship between the major and minor principal strains before failure could well be represented by a single curve. This is not shown as all the data for all tests is very close. Figures 3.19 and 3.20 includes the authors data o f Figures 3.17, 3.18 and are compared with the average curves o f other workers using the DSC Rodriguez (1977) [loose sand samples only], Wong (1986)

and Dalili (1991). Average curves are also included for tests in the Biaxial Tester by Ogunbekun (1988). It can be seen there are slight differences between the average curves obtained by different researcher. The data obtained by the author is within the spread. All workers used heighten Buzzard sand with the same dense and loose voids ratios.

It was considered necessary to compare the data obtained from the DSC with that o f the Biaxial Tester at this stage, as later tests carried out on powder with the DSC were compared with the results o f those obtained using Biaxial Tester.

It can be seen from Figures 3.19 and 3.20 that in general, tests in the Biaxial Tester have a slightly stiffer stress-strain response than in the DSC.

3.8.4- Distributions o f strain within samples

When verifying any complex shear device performance, the importance o f measuring strain distribution within a sample is essential. The uniformity o f strain within a sample sheared in the DSC could be quantitatively evaluated by using strain data obtained within each o f the 7x7 grid areas (Figure 3.13 ) used for strain measurements (Arthur and Wong, 1985). A uniform distribution o f strain implies that an initially homogeneous sample has been subjected to uniform stresses across a boundary. Figures 3.21 and 3.22 illustrates the magnitudes and distribution o f major principal strains measured in a dense sample sheared to R=6.8 with v|/=30° and in a loose sand sample sheared to R=3.5 at \|/=20° respectively. Each printed strain in the Figures 3.21 and 3.22 represents the average o f four strain calculations made from four triangles defined by the square grid o f four adjacent markers (Figure 3.13 ). The average for the

different zones within the samples yielded approximately constant mean strains o f 2.55% and 6.3% for the dense and loose samples respectively. This illustrates the uniformity o f the deformation within the samples.

A well established method o f assessing scatter in data is the coefficient o f variation, a parameter which is defined as the standard deviation divided by mean value.

Figures 3.23 and 3.24 illustrate the coefficient o f variation o f the major principal strain for four dense and loose samples using strain data from Area 2 (central 25%) o f the sarhple respectively. Samples were sheared monotonically under different principal stress directions. In these figures the coefficient o f variation corresponding to the system accuracy is shown by the hatched zone. The system accuracy is obtained by comparing two radiographs o f the same grid with no intervening grid distortion (Wong and Arthur, 1985). This gave a standard deviation 0.10% and the system accuracy line was drawn by dividing the standard deviation ( 0.10%) by an assumed major principal strain. This relates to a material which does not strain and reveals the accuracy o f the measuring system. The actual experimental data should plot above this zone. This implies that a repeat o f 0.10% standard deviation is not possible on the straining material and the data obtained may be best described by the 0.5% standard deviation curve which is obtained in similar way as to that o f 0.10% system accuracy curve. This could be seen as measure of inhomogeneity within the straining samples when one considers the particulate nature o f the sand sample.

The coefficient o f variation is dominated by the measurement uncertainty at major principal strain magnitudes less than 0.5% and only when the measured strain approaches 1.5% it is controlled by the sample behaviour. Figures 3.23 and 3.24 show

that the coefficient o f variation with strain decreases from its initial value to a minimum and settles down as the strain proceeds except for dense samples (Figure 3.23) in which the coefficient o f variation starts to rise again with larger deformation . This is an indication o f increasing non-uniformity in the sample as it approaches failure and the potential development o f failure plane.

3.8.5- Direction o f principal stress and strain

With a knowledge o f normal and shear stresses acting on the boundary o f a sample during a DSC test, the directions o f principal stresses were obtained using the following equation (Figure 3.15.b)

tan 2\j/=2'Cx/(ax-(Jy)

where \\f was the angle that the major principal stress made with the y-axis (Face o f sample). Although the principal stress directions in each DSC test were calculated from the applied boundary stresses, the directions o f principal strain increments were found from the displacement o f the markers (7x7 grid) on successive radiographs. There should be coincidence o f axes o f stress and strain increment when samples were prepared in the direction o f the o f plane strain and were tested under a fixed direction o f major principal stress. Figure 3.25 defines the axes o f applied principal stress direction and measured principal strain increment direction and the deviation, A between them.

The deviation o f axes o f principal stress and strain increment can be used as an additional indication on the operational performance o f the DSC. Coincidence o f the axes ensured the correct combination o f normal and shear stresses were being applied

Figures 3.26.a and 3.26.b show the data obtained from both dense and loose samples respectively. It can be seen that at the initial shearing stage o f each test the deviation o f the measured strain increment direction and applied principal stress direction are within ± 4°. This reduced to ± 2° as the magnitude o f principal stress increased. These data are also comparable to ±5° and ±2° deviation obtained by Wong (1986) and Dallili (1991) respectively.

3.9- Verification o f the apparatus operational performance

The monotonie tests data presented in this section (Figures 3.17 and 3.18), illustrate the stress and strain curves o f dense and loose sand samples sheared with different fixed orientations o f major principal stress direction. The results show that the required operational technique regarding sample preparation, operating procedures and strain measurements were achieved and were comparable with other researcher's data (Figure 3.19 and 3.20). It also indicated the apparatuses capability to successfully impose a principal stress in any direction \\f (Figure 3.15.b) between 0° to 90° with a given stress path.

The strain computation o f small elements within the samples provided means o f assessing the magnitude, direction and distribution o f the strain in the samples (Figure 3.26.a and 3.26.b ). This enabled the uniformity o f strain and coincidence o f axes o f stress and strain increment to be examined.

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Figure 3.1: Different stages of preparing sand sample membrane ; (a) grid draw n on the membrane, (b) sample membrane in the cubic box and aluminium strips in position, (c) Evo-stik adhesive on one face of the rubber membrane and (d) filling the space between the two aluminium strips.

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