A new broad gauge railway track is being laid using $13\text{-meter}$ long rail sections. The specified sleeper density is $M + 7$, where $M$ is the length of one rail in meters. Calculate the number of sleepers (ties) required for one rail length and the total number of sleepers needed for a $5.2\text{-kilometer}$ section of single track.

A standard gauge railway track (gauge width $G = 1.435 \text{ m}$) has a horizontal curve with a radius ($R$) of $800 \text{ meters}$. If the average speed ($V$) of trains navigating this curve is $120 \text{ km/h}$, calculate the equilibrium cant (superelevation) required to perfectly balance the centrifugal force.

A $10\text{-kilometer}$ double-track railway is being constructed using standard $60\text{ kg/m}$ (often called UIC 60) steel rails. Calculate the total weight of the rail steel required for this project in metric tonnes.

During a routine inspection of a heavily trafficked freight line, a track engineer notices that the expansion gaps between jointed rails have completely closed up at the bottom of a steep grade, while the gaps at the top of the grade have widened excessively. In some areas, the sleepers (ties) are skewed out of square. Identify this phenomenon, explain its primary mechanical causes, and suggest mitigation strategies.

A railway agency is experiencing frequent "mud pumping" (where wet soil squirts up through the crushed stone) and track geometry degradation on a section of track laid over a clay subgrade. The existing track structure consists only of rails, wooden ties, and a $300\text{ mm}$ layer of coarse granite ballast directly on the native clay. Recommend a structural design change to the substructure to solve this chronic issue.