Epicentre Location and Liquefaction Risk for an Alluvial Town
Three seismic stations around an Assam town recorded a shallow earthquake. Station A recorded the P-wave at 10:00:12 and the S-wave at 10:00:24. Station B recorded P at 10:00:16 and S at 10:00:24. Station C recorded P at 10:00:09 and S at 10:00:24. Assume a P-wave velocity of 6.0 km/s and an S-wave velocity of 3.5 km/s. The focal depth is estimated as 15 km. The town nearest the calculated epicentre has 4-5 storey unreinforced brick buildings founded on 12 m of loose, saturated sand; the water table is 2 m deep. The last major earthquake in the region was in 1950. A builder proposes ordinary strip footings with no ground improvement.
1. Calculate the hypocentral distance for each station from the S-P times. Then explain how the three distances locate the epicentre and why this is not yet a complete hazard assessment.
Read the worked answer
Use d = (tS - tP) / (1/VS - 1/VP).
1/VS - 1/VP = 1/3.5 - 1/6.0 = 0.2857 - 0.1667 = 0.1190 s/km.
Station A: tS - tP = 12 s, so d = 12 / 0.1190 = 100.8 km. Station B: tS - tP = 8 s, so d = 8 / 0.1190 = 67.2 km. Station C: tS - tP = 15 s, so d = 15 / 0.1190 = 126.0 km.
These are hypocentral distances. For a 15 km focal depth, approximate epicentral distances are sqrt(d^2 - 15^2): A about 99.7 km, B about 65.5 km, and C about 125.1 km.
On a map, circles centred on A, B and C with these radii intersect near the epicentre; station B is closest. The intersection is not a complete hazard assessment because it gives only location. We also need magnitude, depth, rupture geometry, attenuation, local site response, building vulnerability and population exposure.
2. Assess the liquefaction potential at the town and evaluate the builder's proposal of ordinary strip footings without ground improvement.
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The town is highly susceptible to liquefaction. The critical combination is loose, saturated sand, a shallow water table at 2 m, and a thick 12 m granular layer. A shallow earthquake close to the town would produce strong shaking, and the 1950 event shows the region can generate damaging ground motion. Without penetration tests, the exact factor of safety cannot be calculated, but the site conditions are unfavourable enough to require treatment.
Ordinary strip footings are a poor choice. During liquefaction, the sand loses shear strength, so strip footings can settle differentially, tilt or punch into the ground. Light buildings may float upward if buoyancy exceeds resistance.
Acceptable options include ground improvement by compaction or stone columns, a raft foundation designed for reduced bearing capacity, or deep foundations taken below the liquefiable layer. Drainage and site grading can help, but they do not replace a proper liquefaction analysis. The builder should be required to obtain SPT or CPT data and shear-wave velocity profiles before foundation design is approved.
3. Recommend a monitoring and design programme before reconstruction, including the data that would most change your assessment.
Read the worked answer
Install a strong-motion accelerograph and groundwater monitoring wells before reconstruction. Carry out SPT or CPT boreholes, grain-size analysis, shear-wave velocity testing and a site-specific liquefaction analysis. Map the base of the loose sand and the depth to firm material, because a shallow firm layer would make deep foundations more practical.
The most influential new data would be a high SPT resistance or dense gravel layer within 5-8 m of the surface, which would reduce liquefaction risk, or evidence of a very loose layer extending below 15 m, which would make ground improvement expensive and favour relocation or deep piling. Groundwater fluctuations also matter: a rise from 2 m to 1 m would increase susceptibility.
Design should follow a modern seismic code, with ductile detailing, lightweight roofs, reinforced foundations and a clear evacuation plan. Monitoring should continue through at least one monsoon and one earthquake cycle, with public reporting of results.