Ellen Marsh

2nd Year Soils Laboratory – Drained Triaxial

An investigation into the shear strength of a sand sample in a drained triaxial test

Abstract Four experiments were carried out under different pressure conditions using the same soil sample of fine granular sand. The results gave an average friction angle of 46 degrees, and also reasonably similar shear angles to those measured once the sample had failed were found showing some accuracy in the experiment. The results determined that the higher the effective stress and deviatoric stress of the sample, the higher the maximum shear strength and therefore a stronger soil.

Introduction The drained trixaxial test allows the pore pressure u and the cell pressure to remain constant throughout the experiment and therefore by measuring displacements and the force being applied to the sample you can determine the effective stress and the maximum deviatoric stress at failure. Once the effective stresses have been determined a Mohr’s Circles can be drawn to calculate the shear and friction angles at failure.Three corrections are applied to the calculated deviatoric stress: an area correction, a membrane correction and also a drain correction. These allow for errors caused by the change in conditions that the apparatus create. The formulae for these corrections are given in the Appendices section of the report.

Experimental Method

Figure 1 Essential features of a typical triaxial cell (BS:1377-8)

Ellen Marsh

The sample of fine granular sand was prepared in accordance with BS:1377-1 and was then separated into four for each group/pressure condition being tested. Figure 1 shows the apparatus used for the experiment in accordance with BS:1377-8. Each group were given different pressure conditions to perform the experiment under. Certain conditions had to be maintained to prevent ballooning and the sample failing prematurely, the most important was to ensure that the pressure on the outside of the sample was always lower than the sample itself. It is also assumed that the volumetric strain is zero for this experiment.

Results

Figure 2: The scatter graph shows the results of the four experiments using the same soil sample but each performed under didn’t pressure conditions: these conditions are displayed in the table below.

Figure 3: The chart displays the Mohr's circles representing the conditions at failure for each of the pressure conditions with a calculated average friction angle displayed. The effective stresses were taken from the results table below, and the shear friction angles were calculated from this graph.

Cell Pore qmax Peak Minor Major Effectiv Calculate Calculate Measured

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18-100

0

100

200

300

400

500

600

700

800

900

Axial Strain

Dev

iato

ric

Stre

ss, q

(k

Pa)

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Pressure (kPa)

Pressure (kPa)

Deviatoric Stress (kPa)

Principal Stress σ'3 (kPa)

Principal Stress σ'1 (kPa)

e Principal Stress Ratio (σ'1/σ'3)

d Friction Angle (degrees)

d Shear Angle (degrees)

Shear Angle (degrees)

Group 1 300 250 304 50 361 7.22  49 70 ≈60Group 2 300 200 567 100 674 6.74  48 69 62

Group 3 350 150 831 200 1038 5.19  45 66 65

Group 4 250 100 713 150 870 5.80  43 67 63

Average shear angle was calculated as 46 degrees.

Discussion Figure 2 plotting the deviatoric stress until the axial strain shows that each sample acts plastically initially under any given pressure condition at a similar, in most cases until approximately 0.01 axial strain where the soil then starts to behave elastically. An observation at this initial stage is that the higher the minor principal stress the higher the deviatoric stress at the elastic stage of the experiment.

The rate of increase of deviatoric stress then decreases in each of the samples until it reaches the peak deviatoric stress where the sample fails. At this stage the decreases at a similar rate to how the soil increased. The experiment was then stopped once the deviatoric stress had reached 90% of the maximum. The samples with a larger minor principal axis (which is also the difference between the cell pressure and pore pressure) failed at a higher strain and deviatoric stress. This tells us that the higher the minor principal axis the higher the shear strength of the sample.

The patterns in figure 2 are as predicted and expected of a dense sample in a drained triaxial test. However, there are a few visible anomalies in the data (for example group 3) which could have been caused by a number of human errors. The possible errors in this experiment are the variation in densities of the sample and also human error in reading the displacements and forces from the apparatus. The four groups prepared their sample separately and therefore each group managed to compact a different amount of sand into each membrane, with four densities the samples differed slightly accounting in slightly varying experiments and therefore results. Due to the rapid rate of the experiment at its initial stage, readings were taken every few seconds (these frequencies differed for each group) and each the force and displacement readings were taken by different members of the group and therefore may have not been recorded at the same time and the rate that at which the readings were changing made it difficult to choose a value to record. Another small cause of error would have been in fluctuations of the cell pressure and pore pressure, they were kept to within 1kPa of the target for the duration of the experiment therefore the small changes will have caused a minor error in the results.

The average shear angle was larger than expected, this may be due to group 1’s sample ballooning and therefore affecting the results. This also meant that an

Figure 4: The above table displays the key calculations and also the measured shear angle that was taken during the experiment to compare with the calculated values from Figure 3.

Ellen Marsh

approximate friction angle had to be predicted once the sample had failed. The shear and friction angles were calculated by trigonometry. The differences in the calculated friction angles and the measured friction angles were relatively small taking into account errors caused in the experiment. There is also an additional error of measuring the friction angle by hand using a protractor.

Conclusion

The results showed that the higher the minor principal stress of the sample, the higher the maximum deviatoric stress and therefore shear strength and overall strength. The average friction angle and shear angle were calculated to be 46 degrees as 68 degrees and the difference between these calculated angles and the measured angles is due to experimental and human errors during the experiment.

Appendices Formulas used in calculations taken from BS:1377-8 Methods for test for Soil for Civil Engineering purposes - Part 8: Shear Strength Tests (effective stress):

Axial Strain (8.4a) ε = ΔL/Lc

Area of cross section of the specimen normal to its axis (8.4c)As = ((1-εv)/(1-ε))Ac

Applied axial stress (8.4e)(σ1-σ3)m = (P/As) x 1000

Membrane correction(38/D0) x (tm/0.2)

Drain correction (Table 2, 8.4g) Using the average diameter of 70mm, a drain correction value of 5kPa has been used.

Corrected deviator stress (8.4h)(σ1-σ3) = (σ1-σ3)m –σmb – σdc

Effective major and minor principal stresses (8.4j)σ1’ = σ1 – uσ3’ = σ3 - u