Prism Movement Rate Calculator
Work out the velocity of a survey prism between two monitoring epochs. Geotechnical engineers and mine surveyors use prism movement rates on open-pit walls, TSF embankments and unstable slopes to compare against Trigger Action Response Plan (TARP) thresholds.
Enter Values
Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Enter the cumulative displacement of the prism at reading 1 (d1) and reading 2 (d2) in millimetres.
- Enter the elapsed time between the two readings in days (Δt).
- Optionally enter the previous interval's rate to see whether the slope is accelerating, steady or decelerating.
How it works
The movement rate (velocity) is the change in cumulative displacement divided by the time between readings: v = (d2 − d1) / Δt, in mm/day. Because both figures are cumulative movement of the same prism, their difference is the movement over that interval. The tool also expresses the rate per week (×7) and per hour (÷24).
If you supply the previous rate, the tool reports acceleration = v − v_prev. Accelerating movement is the classic precursor to slope failure, so most TARPs escalate on rate AND acceleration together.
Worked example
A prism moves 15 mm over 5 days. With d1 = 10 mm and d2 = 25 mm, total displacement is 15 mm. Over Δt = 5 days the rate is 15 / 5 = 3 mm/day (21 mm/week, 0.125 mm/hour). If the previous rate was 2 mm/day, acceleration = +1 mm/day per interval — the slope is accelerating.
Common mistakes
- Entering per-interval movement instead of cumulative displacement — d1 and d2 must both be totals from the same baseline.
- Mixing up the time unit: Δt is in days, so a 12-hour interval is 0.5 days.
- Ignoring the sign — a negative rate means the prism recovered or relaxed, not that movement stopped.
Frequently asked questions
What is a prism movement rate?
The velocity of a monitoring prism — how fast a point on the slope is moving, in mm/day (or per hour/week), from the change in cumulative displacement over the time between two survey readings.
Why does acceleration matter more than the rate itself?
An accelerating rate (velocity increasing reading-on-reading) is the recognised precursor to slope collapse. Inverse-velocity failure prediction is built on this trend, which is why TARPs trigger on acceleration.
How do I convert mm/day to mm/hour?
Divide by 24. A rate of 3 mm/day is 0.125 mm/hour. For mm/week, multiply the daily rate by 7.
Can the rate be negative?
Yes. If d2 is smaller than d1 the prism moved back toward its start (recovery, drainage or survey noise). Persistent negatives usually mean scatter rather than real reversal.
What is a TARP?
A Trigger Action Response Plan sets movement-rate and acceleration thresholds (green/amber/red) with defined actions at each level. This calculator gives the rate and acceleration to compare against your site-specific bands.
Related tools
- Prism Movement TARP Checker
- Cumulative Movement Calculator
- Rolling Average Movement Calculator
- Crack Displacement Calculator
- Piezometer Trend Calculator
- Radar Prism Displacement Comparison Tool
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Tip: Enter any known values to calculate the remaining results.
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