DETERMINAR EL NIVEL DE EVASIÓN TRIBUTARIA POR LA

THE DSC

4.1- In tro d u ctio n

This chapter describes the development o f a procedure to test powder in the DSC. This research study was the first which the DSC was used to test powder.

Dry white Kaolinite powder was chosen as the material to be tested.

The dry and highly compressive nature o f the loose powder made it necessary to modify the DSC and to develop a testing procedure to limit strains when subjecting samples to shear under plane strain conditions while producing reliable stress-strain data. The DSC works best under small strains and was not designed to cope with excessive strains.

Major components o f the DSC remained unchanged to that described in Chapter 2. However alteration to some o f the components were necessary for the reasons explained later in this chapter.

A general description o f stress path is also given in this chapter as an aid in describing the different forms o f stress application.

The sample preparation method is also described in detail in this chapter. The preparation method involved com pressing layers of pow der to a know n stress into a hollow cubic sample preparation box in the direction o f deposition shown in figure 4.1.a . This m ethod m ade it necessary to p re p a re sam ples w ithin the DSC.

Finally this chapter describes a preliminary set o f shear tests on the powder. The data obtained from these tests concluded that the sample preparation method and test procedure resulted in comparable results obtained by other workers ( M. Jamebozorgi,

1997 and L.P. Maltby, 1993).

4.2- G eneral Stress P ath D escription

First loading o f the samples took place whilst samples were being prepared. This applied .loading was in a direction orthogonal to the subsequent plane o f strain o f the samples ( Figure 4.1). Subsequent loading occurred in the plane o f strain (Figure 4.1.b). Only stress paths in the plane o f strain are described in this chapter. The biggest and smallest principal stresses in the plane o f strain are termed the major (cji) and minor (cr^) principal stress respectively. The principal stress orthogonal to this plane is termed the intermediate principal stress (02).

The magnitude o f the major and minor principal stresses on an element in the plane o f strain can be represented by the Mohr Circle drawn in a , i axes ( Figure 4.2.a). Point (a) the top o f the circle can also be used to describe the stress on an element with

aa = (cTi + a3 )/2

Ta = ( o i - Ç J 3 ) / 2

A stress path will describe the movement o f top o f the Mohr circle and indicates the changes to the state o f the major and minor principal stresses. The stress paths that were most commonly followed are given in Figure 4.2 .

Stress path AB along g axis ( Figure 4.2.b) shows that a sample was loaded from A to B with (T;=(73. All samples were subject to this stage termed the "Biaxial

Consolidation" stress path. At B, a i= a3=ac where represents the magnitude o f greatest stress during this stage o f the stress path.

Figure 4.2.c shows two stress paths AB and BC. Stress path AB is the biaxial consolidation which was described above. Stress path BC shows shearing o f the sample where it starts at point B and shearing continues along BC with no change to

Gi=Gc with decreasing g2 until failure was reached. This stress path is at -1 slope to

the cj axis.

Figure 4.2.d also includes two stress paths AB and BD.

Stress path BD which is a Vertical stress path, shows the state o f stress at the start o f the shearing process described by point B and, at every point along BD the shearing continued by increasing G\ and decreasing dg such that (cF; + g^!2=g^ constant.

It is important to note that the stress path description is not complete as it does not give information about the direction o f major principal stress in the plane o f strain. The direction o f the major principal stress \|/ is defined in Figure 4.1.b. It is also important to point out that the manner in which the stress path has been described indicates that the major and minor principal stresses during the shearing process always operate in the plane o f strain with the intermediate principal stress acting orthogonal to it. The following paragraph is an attempt to clarify some confusion which may arise from this.

During the preparation and preliminary stage o f the shear tests the magnitude o f the principal stress orthogonal to the plane o f strain or, what was described as intermediate principal stress "CF2" was recorded. Measurements o f the stresses taken throughout tests showed that at an early stage o f the shearing process the intermediate and minor principal stresses did not operate in their respective planes but as samples

continued to deform, the major and minor principal stresses were operating correctly in the plane o f strain with intermediate principal stress on it well before failure took place. Although this description does not follow convention precisely it is thought to be less confusing in the long run.

4.3-Pow der sam ple p re p a ratio n

To enable preparation o f samples within the DSC, it was found necessary to replace the water filled plane strain bag which was part o f the base with a solid bottom platen. This platen was moved to become the upper plane strain face.

The sample preparation technique is very similar to the preparation method for experiments performed with the Biaxial Tester ( Ogenbekun, 1988).

The method involved the use o f a cubic hollow acrylic sample preparation box ( Figure 4.3.a) o f size 106 x 106 x 100 mm (The 100 mm dimension being the distance between the plane strain faces.) into which was placed a sample membrane o f the same dimension and located centrally on the DSC base. This allowed a sample to be prepared in the direction o f the subsequent intermediate principal stress. Preparation was by depositing (Figure 4.3.b) and compressing layers o f the test material with a plunger ( Figure 4.4). The plunger had a water filled cushion which was used to achieve a constant uniform applied pressure. Sufficient test material to fill about 20mm depth was loosely scooped into the box and a spatula was used to ensure that every com er o f the sample space was filled and that the material was approximately levelled. The plunger was lowered to compress this quantity o f material to a known stress by using weights placed on the plunger. The magnitude o f this stress was set to

An acrylic template with holes at equal intervals was gently lowered onto the level powder and using this, a square grid (7x7) o f tungsten ball bearings spaced at 12mm was placed on the powder surface ( Figure 4.5). The template was then carefully removed and then all the ball bearings stabilized by pushing them gently into the powder surface.

Filling and compacting continued to completion o f the sample preparation. The top surface o f the sample was then levelled. The preparation box was carefully unscrewed and removed leaving the sample enveloped by the sample membrane and at the centre ofD SC .

4.4- Test P ro ced u re

After sample preparation was completed the normal pressure bags were gently positioned around the sample and with great care to not disturb the sample. This necessitated a small squeezing o f the normal pressure bags between the sample membrane and the backing plates carefully ( Figure 4.6.a). This squeezing enabled all normal pressure bags to move towards the sample when samples were subjected to stress path AB ( Figure 4.2) and also to help maintain sample integrity whilst the top platen or water filled plane strain bag was positioned and locked in place.

When the water filled reinforced plane strain bag was used, it was as a constant volume sensor to measure the intermediate principal stress and to indicate that general plane strain conditions were operating during shear. After this verification the water filled plane strain bag was replaced by a solid top platen.

Prior to positioning the top platen or water filled plane strain bag were first carefully cleaned, evenly spread with a coating o f grease and then covered with two thin rubber

sheets already coated with the same grease. The face o f the second rubber sheet which was in contact with the sample was kept grease free.

After the top platen was positioned a radiograph o f the sample was taken, developed and fixed. Then stresses were applied following stress path AB ( Figure 4.2) with small incremental increases in all four normal pressure bags until a stress o f 5kpa less than the desired stress was reached. At this stage shear sheets may or may not be placed around the sample. For tests in which v|/ was equal to 0° or 90° the use o f shear sheets could be avoided. If this was to be the case the stresses were further increased to the desired stress at which stage stress paths are chosen to shear the sample. If the shear sheets were to surround the sample, at reaching a stress o f 5 kpa less than Cg on the stress path AB ( Figure 4.2 ), the biaxial stresses were decreased to 0 kpa and top platen was very carefully removed. Then all normal pressure bags were removed from all four sides o f the sample while ensuring that the sample was not damaged. At this point because the sample was biaxially compressed the sample membrane was bigger than the actual sample. The four vertical sides o f the sample membrane were cut and removed ( Figure 4.6.b ). Then the shear sheets were set loosely around sample and the specially prepared edges were positioned at the two comers o f the sample where the shear sheets emerge ( Figure 4.7.a ). The shear sheets were then gently tightened around the sample and the normal pressure bags and top platen relocated (Figure 4.7.b ). The sample, with shear sheet around it, was reloaded along the biaxial stress path AB and the normal stresses were increased incrementaly to the desired stress

The procedure described above was necessary as the sample size has to be very close to the size o f the shear sheets sleeves when applying shear stresses to the sample faces. This initial procedure ensured that almost all the volumetric compression had taken place before the shear sheets were placed. The additional 5 kpa compressive stress enabled the shear sleeves to bed securely to the sample.

On reaching a stress o f the shearing process started in which the sample faces were subjected to both normal and shear stresses according to the chosen stress path and major principal stress direction. The experimental operation required in following the deformation o f the sample during increasing boundary stresses were very close to those described in Chapter 3. Allowance for angles o f distortion ( a , and Pi ) o f the deforming sample( Figure 3.16) was included after x-rays o f the grid o f tungsten balls set in the samples could be examined. As these angles were very small at early stages o f shear, this adopted procedure made little difference to the early calculated values o f stresses. Only when near to failure were the values o f and pi big enough to cause a change in intended stress path. An example o f how this allowance were made is given in Section 4.6.2.

Radiographs were taken at stages during tests for sample strains to be computed. Tests were terminated on the onset o f failure planes prior to complete sample instability. Only strain o f data from radiographs prior to that containing failure planes was used to compute strains within the samples. The very last strain data obtained for each test corresponds to the state o f the sample just before failure took place. The radiographs with failure planes helped to relate orientation to angle o f friction.

4.5- Preliminary Tests on Powder

These series o f tests were to establish that reliable stress-strain data for powder could be obtained using the DSC. Confirmation o f the reliability o f the data obtained using the DSC was shown when comparing results o f shear tests using the Biaxial Tester. The Biaxial Tester results were obtained using the same material and sample preparation method, stress path and stress level ( M. Jamebozorgi, 1997).

4.5.1- Constant Direction Monotonie Shear Tests

These are shear tests in which the directions o f the principal stresses are held constant until failure is reached.

The direction o f the major principal stress (vj/) is defined in Figure 4.1.b. The general stress path for this series o f tests is shown in Figure 4.2.d. More detail o f stress magnitude is shown with each test description.

4.5.1.1- Series 1 : Tests with the major principal stress direction \|/=0° or 90°.

These tests may be considered to be biaxial tests in which principal stresses are applied to sample faces.