Is the Mountain-Front Fault Capable? Slip Rate, Magnitude, and a School Setback
A 3.2 km-long, north-striking, east-dipping normal fault is mapped along a mountain front. Aerial imagery shows a 2–4 m high scarp across a late Pleistocene alluvial-fan surface. A trench cut across the scarp exposes a 4,200 ± 300 yr BP charcoal-bearing deposit displaced 1.1 m vertically in two separate surface-rupturing events, each of about 0.55 m of throw. Regional GPS records 2 mm/yr of distributed extension across a 40 km wide zone. The fault lies 2 km from a 60 km-long range-bounding master fault with a documented late Holocene rupture. A school is proposed on the fan, 150 m from the mapped trace.
1. Determine whether the fault should be treated as capable for design purposes, and rank the evidence by how decisive it is.
Read the worked answer
Yes - treat it as capable.
Evidence, most to least decisive:
- Trench evidence of surface rupture in a datable Holocene deposit. Two events displacing a 4,200 yr BP unit, with the younger event breaking the ground surface. This is the only line of evidence that directly establishes recurrence and near-surface rupture; geomorphology alone could be argued as a landslide scar or a construction feature.
- The 2–4 m scarp cutting the fan surface. Independent corroboration, and it shows cumulative displacement, not a single event - the deposit interval alone would not have captured the older history.
- Tectonic setting and proximity to a 60 km master fault. Provides the mechanical plausibility and, more importantly, means the hazard is not limited to this 3.2 km strand.
Cautions that must appear in the report:
- The scarp height (2–4 m) exceeds the 1.1 m measured in the trench; the difference records older events not exposed or fan-surface age effects. Do not use trench displacement to explain the whole scarp.
- The trace may be concealed between the mapped extent and the site. A fault under 2–5 m of fan alluvium leaves no surface expression, so the mapped trace is a minimum extent.
By any common regulatory test - displacement at or near the surface within the Quaternary, or repeated movement in the recent geologic past - this fault qualifies.
2. Calculate the vertical slip rate and recurrence interval, compare them with the regional extension budget, and estimate the maximum magnitude both for this fault alone and for a linked rupture.
Read the worked answer
Slip rate and recurrence:
- Vertical slip rate = 1.1 m / 4,200 yr ≈ 0.26 mm/yr
- For a normal fault dipping ~60°, net slip = 0.26 / sin 60° ≈ 0.30 mm/yr, and horizontal extension = 0.30 × cos 60° ≈ 0.15 mm/yr
- Recurrence = 4,200 yr / 2 events ≈ 2,100 yr (interval ~2,100 yr, so the elapsed time since the last event is worth comparing against it - a rough probability can only be stated as a long-term rate, not a prediction)
Against the regional budget: 2 mm/yr across 40 km is a distributed strain budget shared among many structures. This fault's 0.15 mm/yr of extension is roughly 7–8% of the total - entirely plausible for one splay among several, and it shows the budget does not contradict a 0.26 mm/yr vertical rate.
Magnitude, two ways (M = 5.08 + 1.16 log L):
- Isolated 3.2 km rupture: 5.08 + 1.16 × 0.505 ≈ M 5.7
- Linked rupture with the 60 km master: 5.08 + 1.16 × 1.778 ≈ M 7.1
The ≈1.4 magnitude-unit gap is the whole point. A D5.7 event with 0.55 m of surface slip would be locally violent but limited in footprint; a linked M7.1 rupture would shake the site for far longer and could rupture the splay itself. Design should not be based on the short length alone - length-magnitude scaling applies to the rupture, not to the mapped segment.
3. Given a 150 m separation from the mapped trace, recommend a setback and any further work required before a school is sited there.
Read the worked answer
Recommendation: do not site the school at 150 m without further work; prefer an alternative site off the fan.
Reasoning:
- Surface rupture is the controlling hazard, and a 150 m offset provides no protection against it. The trace is mapped where it is visible. Under 2–5 m of fan alluvium a splay would be invisible, and the trench showed two events, one of which reached the surface - so a rupture could daylight anywhere in the fan, not just at the scarp.
- Regulatory setbacks are typically 15–50 m from a known trace; that figure assumes the trace is located. For a critical facility with a dependent population, the defensible approach is either a large setback (well beyond the width of a possible rupture zone plus lateral spread) or relocation.
- Secondary hazards on the fan: the same 0.55 m of coseismic throw would shake a fan built of loose alluvium - liquefaction and dry ravel or rockfall from the mountain front are both credible.
Work required if the site is retained:
- A fault-investigation trench or shallow geophysics (GPR, seismic reflection) across the school footprint itself, not just at the mapped scarp, to search for concealed splays.
- A geotechnical program for liquefaction and slope stability on the fan deposits.
- If a splay is found beneath the footprint, relocate; if not, document the search and set the building back from the entire investigated zone, with the setback measured from the outermost splay.
The sound professional position is that 150 m is a number, not a safety margin, and the school is the wrong building on which to test it.