*7.6.1 Settlement*

Vertical and horizontal displacement of structural layers is an important problem in ballasted railways that cause noticeable geometry change, reduce maintenance intervals, and consequently increase maintenance costs. The RRP235special stabilized clayey soil can replace the ballast underneath the sleepers. This led a significant reduction of displacement in vertical and horizontal directions. The specimens with different dosages of additives were made in special boxes and tested using a ballast box device. **Figure 18** shows the specimens after 100,000 cycles of loading.

The ballast box test was carried out on the samples, and as rendered in **Figures 19** and **20**, the additive is an influential factor in the strengthening of clayey soil. Reverse to the static tests pattern, the sample with 0.15 lit/m<sup>3</sup> has the least amount (2 mm), and the specimen with no additive has the largest amount (4.7 mm) of settlement. Use

### **Figure 18.**

*Ballast box samples after testing (specimens from left to right correspond to 0, 0.09, 0.15, 0.21, and 0.27 lit/m<sup>3</sup> of RRP235 Special).*

**Figure 19.** *Settlement diagram.*

*Developing a Novel Superstructure System for the Ballasted Railways Using RRP235special... DOI: http://dx.doi.org/10.5772/intechopen.111470*

**Figure 20.** *Settlement of samples in cycle 100,000.*

of RRP235special causes more than 57% reduction in vertical displacement. Therefore, the dosage of 0.15 lit/m<sup>3</sup> was selected as the optimal amount in terms of settlement in the ballast box test.

The exodus of interlayer water due to ion exchange gives improved compaction to the stabilized soil and is the main factor of strengthening, but increased additive results in excess of free ions around the colloids, which renders negative properties [43].

### *7.6.2 Stiffness*

The stiffness of the track is affected by the materials used. Any change in material type causes a change in stiffness. Using the ballast box test, the stiffness of clayey soil with different additive dosages has been evaluated. According to the RRP235special action, the results are predictable. As shown in **Figure 21**, the sample with 0.15 lit/m<sup>3</sup> RRP235Special has the highest stiffness, and the sample with no RRP235Special has the lowest. Low and high stiffness limits have been shown in **Figure 21** by 30 and 80 kN/ m, respectively [40]. The specimen with 0.15lit/m<sup>3</sup> has the best result and is selected as the optimal value for stiffness.

### *7.6.3 Damping ratio*

Comparing different amounts of RRP235Special, the damping ratio of each sample, which is representative of the lost energy, divided by the energy input in a cycle, has been determined using eq. (2), proposed by Jacobsen [44];

$$
\xi = \frac{\Delta E}{2\pi \text{Kx}^2} \tag{2}
$$

### **Figure 21.**

*Stiffness of samples with different dosages of RRP235Special.*

Where Δ*E* is the dissipated energy, and *k* and *x* refer to the stiffness and deflection of samples, respectively.

**Figure 22** shows the force–displacement relationship of the sample with 0.15lit/m<sup>3</sup> RRP235 Special at the final cycle (100,000th). The red zone on this graph indicates the dissipated energy. In order to calculate the damping ratio of the samples, the area of this zone should be divided by that of the loop.

### **Figure 22.** *Calculation of damping ratio by means of the force–displacement.*

*Developing a Novel Superstructure System for the Ballasted Railways Using RRP235special... DOI: http://dx.doi.org/10.5772/intechopen.111470*

**Figures 23** and **24** show the force–displacement loops of all samples and their damping ratio values, respectively.

The settlement, stiffness, and damping ratio are interdependent. The damping ratio and settlement are opposite of the stiffness. The specimen with high stiffness has a low settlement and damping ratio. Greater concentration of colloids with the use of additive and ion exchange causes vibration transmission and low damping ratio. So the results shown in **Figure 24** confirm the relation between the specifications. The sample with a high damping ratio behaves better facing dynamic forces and reduces transmitted energy than others. The sample with 0.15 lit/m<sup>3</sup> has the lowest, and the sample with no additive has the highest damping ratio. The sample with no additive was selected as optimal dosage for damping ratio. But the preference for stiffness and settlement cause the challenge of optimal dosage selection. So the dosage of 0.15 lit/m<sup>3</sup> has been selected as an optimal value for dynamic tests.

Samples with different dosages of additive were made, and an optimal percentage was found. As a result, the sample with 0.15 lit/m<sup>3</sup> RRP235Special was determined as the suitable dosage for mechanical and physical tests, while only in the Maximum Compaction test, by increasing the additive, the optimum water content decreased.

### **Figure 23.**

*Piston Force–displacement graphs for five different samples (a, b, c, d, and e are the sample with 0, 0.09, 0.15, 0.21, and 0.27 lit/m3 additive, respectively).*

**Figure 24.**

*Damping ratio of samples with different percentages of RRP235 special.*
