Geological Hazards: Worked Examples

A benchmark tied to a stable external datum was at 15.500 m in 1990 and 13.100 m in 2020. Find the average downward rate in mm/year and the 2050 elevation if that movement rate continues unchanged. Can this one benchmark establish a sewer's future gradient?

At a saturated soil element, total vertical stress is 150 kPa and initial pore pressure is 50 kPa. Total stress remains constant while excess pore pressure rises by 40 kPa. Find the initial and final effective stresses and the excess-pressure ratio.

A different saturated element starts at total vertical stress 160 kPa and pore pressure 60 kPa. The teaching model selects $r_u=1.00$ with constant total stress. Calculate the pressure and effective stress, and assess the claim that every affected soil must now have zero residual strength.

A straight sewer has horizontal length 100.0 m, initial upstream invert 12.000 m and downstream invert 11.500 m. In a 20-year constant-rate scenario, upstream ground settles at 12.0 mm/year and downstream at 3.0 mm/year. Assume each pipe end follows the measured ground movement and horizontal length stays fixed. Find total end movements, differential movement and the final end-to-end gradient.

Enlarge

A horizontal projected roof area of 200 m² carries a uniform 0.100 m ash layer. Use an assumed bulk unit weight of 15.0 kN/m³ for this deposit condition. Find the added vertical load intensity and total load. No roof capacity is supplied.

Enlarge

A specified landslide event has annual probability 0.0500. The exposed highway assets have replacement value PHP 15.0 million; conditional mean damage is 0.800 of that value. Find conditional event loss and expected annual loss. Business interruption and casualties are outside this stated monetary model.

For an illustrative slope treatment, use before/after annual event probabilities of 0.0500 and 0.00100, the same PHP 15.0 million exposure and 0.800 conditional damage fraction. Initial cost is PHP 2.00 million. Treat these probabilities as given scenario estimates, not guaranteed treatment performance. Find expected annual loss reduction and simple payback, excluding maintenance and discounting.

Assume independent annual trials and a constant event probability of 0.0100. Find the probability of at least one event in 50 years. Explain why calling it a once-in-100-years event does not mean the next 99 years are safe after one event.

A fixed reference is 60.0 m landward of today's measured shoreline position. Explore constant retreat rates of 0.800, 1.20 and 1.60 m/year. Find when the idealized shoreline would reach that reference. No cliff-failure model, storm allowance or required planning setback is supplied.

Enlarge

Use the synthetic volcanic-pathway plan from the lesson. A proposed crossing lies on a channel draining volcanic deposits. An alternative site is outside that channel, but no complete hazard study exists. A reviewer claims that distance from the vent proves both sites safe and requires a cable-stayed bridge. Evaluate the claim and identify the needed studies.

Enlarge

Three synthetic observations are reported: sample A expands when wetted under a specified test stress; sample B loses height when wetted at unchanged stress; seepage at site C carries fines. A proposal specifies identical deep foundations at all three sites without further investigation. Identify the likely mechanisms and the missing evidence.