Constant Volume Friction Angle

The LDS test revealed the possibility of investigating the constant volume state. In this state, the composites exhibited stable behaviour in terms of volumetric behaviour, void ratio, normal stress and shear stress. This state was called steady state by (Dove and Jarrett, 2002, Frost et al., 2002, Afzali-Nejad et al., 2017) and residual state by Koerner, (2012) and Tabucanon et al., (1995). Thus, as discussed earlier, the constant volume state was selected for this study. On the basis of the relationship between the normal stress and the constant volume friction angle, the constant volume was calculated as follows (Tabucanon et al., 1995, Dove and Jarrett, 2002, Fioravante, 2002, Lings and Dietz, 2005, Afzali-Nejad et al., 2017):

𝜑𝜑cv = 𝑡𝑡𝑡𝑡𝑡𝑡^-1�^𝜏𝜏_𝜎𝜎^cv� (5.15)

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The same as peak friction angle and maximum dilation angle results, analysing φcv

of composite has been depicted in three main groups. Overall, Figure5- 27(a, b and c) have been shown almost similar results with the deduced friction angles of Figure5- 26. The use of cementitious materials in the sand treatment of the ST class had only a minor effect. Contrast with that, the outcomes of sand-rubber mixtures were shown a significant increment in the friction angle of the composite at the constant volume was.

Once more time, the result suggested the greatest achievement obtaining by a combination of 10% rubber plus 5% of stabilisers. Moreover, the composites of the STR20 class exhibited the most similar improvement among the mixtures, thereby proving the relationship deduced from Figure5- 26. Therefore, sand reinforcement with 20%rubber exhibited more interlocking among the sand and the rubber particles and formed strong composites, as shown inFigure5- 27(c). This process was additionally boosted by combining this mixture with a certain amount of cementitious materials containing finer particles to increase the connections among the composite’s particles.

Resulting from this a composite comprising the characteristics of flexibility, asperity, and cohesion. The further analysis will be described that how the combination of rubber and cementitious material could be stocked the composite’s structure by increasing the attractive intermolecular force.

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Figure5- 27. Results of the constant volume friction angle versus the normal stress of sand composites based on the composite categories: (a) ST class; pure sand and mixture of sand and stabilisers; (b) STR10; sand with 10% rubber and a combination of 10% rubber and stabilisers;

(c) STR20; sand with 20% rubber and a combination of 00% rubber and stabilisers.

φcv= 0.7016σ + 3.051, R² = 0.998 [φcv= 34.7]

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With this in mind, on the basis of the linear equation results of the composites, we formulated the following empirical equation:

φcv = αʹ𝜎𝜎 + β' (5.16)

where βʹ denotes the apparent cohesion of the soil at the constant volume state shear stress, considering a zero dilation angle in the constant volume state. Consequently, the results revealed the effectiveness of additives with respect to the generation of the apparent cohesion in the sand even after a failure. However, the importance of creating a composite with the optimum ratio of additives to achieve the maximum improvement was implied by the results of all the categories. Overall, adding 20% rubber with dosages of cementitious materials has been established the composite with the highest intermolecular force. It seems that, the combination of soil tension (Gratchev et al.) and cementation (Ccm) were significantly kept the particles connection even after the failure. Nevertheless, it does not mean that performing the greater amount of additives resulted in a greater increments. Subsequently, adding five percentages of stabiliser into the composites of both STR10 and STR20 classes, was found to be more effective than addition of 10% stabiliser. It is worth mentioning that, comparing the results of sand composites, treating with either rubber or stabiliser only indicates two different behaviour. Increasing the proportion of the stabiliser added from 5% to 10% reduced the effectiveness of the stabiliser with respect to improving the cohesion of sand at the constant volume. Thus, an increase in the stabiliser content formed a composite with a relatively rough surface, increasing the vulnerability of the surface area. In contrast, increasing the rubber content improved the cohesion of sand after a failure, and the surface roughness of the composite was reduced by the flexibility of the rubber particles. In other words, after a failure, the material with a capacity to create cohesion tension was more effective than a material with the capacity to create cementation cohesion. Accordingly, in a combination of rubber and a stabiliser, increasing the rubber content not only improved the effectiveness of the stabiliser but also minimised

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the loss of the electrostatic force among the composites, because of the increasing stabiliser content.

BRIEF SUMMARY…

A composite’s friction angle at a constant volume exhibited an almost similar behaviour to the maximum friction angle. The addition of cementitious materials for the sand stabilisation of the ST class had only a small effect. In contrast, the use of rubber particles for sand reinforcement showed a significant improvement in the friction angle of the composite at the constant volume. Subsequently, the results revealed the effectiveness of additives with respect to the generation of the apparent cohesion in sand even after a failure. In general, the use of 20% rubber with a certain proportion of cementitious materials formed a composite with the highest intermolecular force. Further, a combination of soil tension (Gratchev et al.) and cementation (Ccm) kept the particles together even after a failure.

On the whole, particles with the flexibility characteristic could be easily moved on the contact surface. Subsequently, the composite exhibited only a minor change in both the mobilised shear strength and the volumetric strain. Associating the capacity of cementitious material for connecting a greater number of particles, in addition of the elastic capacity of rubber particles, leads to generate the composite with a greater strength capacity and significant elastic tension for reducing the dilatancy behaviour.