A square footing is to be constructed on a sand deposit. The footing will be 1.5 m wide ($B$) and placed at a depth of 1.0 m ($D_f$). The average corrected SPT N-value ($N_{60}$) within the zone of influence is 20. Calculate the allowable bearing capacity for a settlement of 25 mm.

A thin-walled Shelby tube has an outside diameter ($D_o$) of 76.2 mm and an inside diameter ($D_i$) of 73.0 mm. Determine the area ratio ($A_R$) and evaluate if the sample is considered undisturbed.

During a subsurface exploration in granular soil, a raw SPT N-value of 15 was recorded at a depth of 5.0 m. The effective overburden pressure ($\sigma_v'$) at this depth is 85 kPa. The test was conducted using a safety hammer ($\eta_H = 60\%$), a standard sampler ($\eta_S = 1.0$), in a 150 mm borehole ($\eta_B = 1.05$), with a rod length of 6 m ($\eta_R = 0.85$). Calculate the corrected value $N_{60}$ and the normalized value $(N_1)_{60}$.

A diamond core drill run of 1.5 meters (1500 mm) yielded the following lengths of intact rock core pieces (in mm): 250, 80, 150, 110, 90, 300, 50, and 200. The remaining recovery consisted of highly fractured pieces smaller than 50 mm. Calculate the RQD for this core run.

A 40-story residential tower is planned in a downtown urban environment where historical records indicate a profile of loose sands overlying thick, compressible marine clay, followed by deep bedrock.

A new highway alignment is proposed through an area known for karst topography, characterized by soluble limestone formations that are prone to sinkholes and subterranean voids.