Chapter 38 Rivers Flood Probability and Slope Stability

Year 2 · Environmental Geology · G225-L2

Interpret hydrographs annual flood probability hill torrents and mass movement using transparent classroom models and safe desk activities.

Water storage and flow connect surface processes and groundwater. Original Geology Hub teaching diagram.

This independent lesson follows topics in the supplied University of Peshawar BS Geology curriculum labelled session 2004–05 onward. It is a learning resource, not an official university course or a statement of current degree requirements.

Learning objectives

Read a conceptual hydrograph and explain runoff controls.
Convert recurrence interval to annual exceedance probability.
Connect slope failure to forces, materials and water.

Floods in their catchment

A hydrograph plots discharge or water level against time. Rainfall, snowmelt, catchment area, soil infiltration, storage and channel geometry affect its shape. The rising limb shows increasing flow, the peak marks the largest recorded value and the recession describes declining flow. An urban catchment can respond differently from a vegetated catchment because paved surfaces and drains change runoff pathways.

Perennial rivers flow for much of the year, whereas ephemeral channels may carry water only after events. A dry hill-torrent channel can still convey a powerful flood. Floodplain deposition, channel migration and bank erosion are parts of the same river system. A historical channel outline is not a guarantee that the river will remain there.

Probability is not a timetable

A 100-year flood is conventionally associated with a 1% annual exceedance probability under the statistical model used. It does not mean one event occurs exactly every century. Successive years can both exceed that threshold. Estimates depend on records, model assumptions and changing catchment conditions. A short series of observations may produce a highly uncertain estimate of a rare event.

Dams, levees, retention areas and channel modifications can reduce some impacts while creating trade-offs or shifting risk. Residual risk remains if a structure is overtopped, fails or is exceeded by an event outside its design assumptions. Flood management therefore also considers exposure, warning and room for water, rather than treating one structure as a complete solution.

Why slopes move

Mass movement occurs when downslope forces overcome resisting strength. Falls, topples, slides, spreads and flows describe different movement styles. Lithology, discontinuities, weathering, slope angle and water influence behaviour. Increased pore-water pressure can reduce effective normal stress along a potential sliding surface, weakening frictional resistance. Undercutting or loading can alter the force balance without changing the rock type.

Record evidence such as scarps, displaced drainage and old deposits from safe public viewpoints or published imagery. Do not approach unstable slopes for a lesson. A desk-based interpretation should distinguish a suspected feature from a confirmed active landslide. Site-specific stability design requires field investigation and professional analysis; a toy slope cannot establish a safe building location.

Calculate discharge and runoff volume

Discharge is cross-sectional area multiplied by an appropriate average flow velocity. An illustrative channel section of 12 m² with mean velocity 1.5 m/s carries 18 m³/s. This assumes the measured section and average represent the flowing water; a single surface speed may not do so. A triangular event hydrograph rising from a zero event-flow baseline to 100 m³/s and returning over four hours has volume 1/2 × 100 × 14,400 = 720,000 m³. Real hydrographs may require subtracting baseflow and summing measured intervals rather than assuming a triangle.

Read a frequency estimate as a model

A simple ranked annual-maximum exercise assigns an approximate return period T = (n + 1)/m, where n is years of record and m is rank from largest to smallest. In a 19-year illustrative record, the second-largest annual maximum has T = 20/2 = 10 years, corresponding to 10% annual exceedance under that plotting convention. This is not a precise guarantee for future flow. Different statistical models, incomplete records and changing land use alter estimates, particularly in the tails. Present record length and assumptions beside the plotted curve.

Link slope style to movement mechanism

A fall detaches material that moves through air; a slide moves predominantly along a surface; a flow deforms internally as it travels. A rotational slump has a curved movement surface, unlike an ideal planar rockslide. Creep is slow deformation that may tilt posts or bend vegetation, but those features can also have other causes. Snow avalanches differ in material and behaviour from soil or rock failures, even when they share gravity as a driver. Examine material, geometry and observed movement rather than classifying every event by its speed alone.

Explain why interventions have limits

Removing material at a slope toe can reduce support, while adding a load near the crest can increase driving forces. Drainage can change pore pressure but may also shift where water emerges. In rivers, a levee can reduce inundation for some events while leaving overtopping and failure risk; channelization can change downstream flow timing and erosion. An intervention should therefore be assessed as part of a connected system. A classroom force-balance diagram helps identify relevant factors but cannot certify an actual slope or flood defence. The defensible output is a model with required evidence and possible trade-offs, not an unsupported declaration that a site is safe.

Worked activity

For an invented stationary, independent annual model with flood exceedance probability p = 0.01, the probability of at least one exceedance in 30 years is 1 − (1 − p)³⁰ ≈ 0.260, or 26%. The calculation illustrates cumulative exposure, not a prediction for a real river.

Sketch two hydrographs with equal total runoff but different peaks. A narrow high peak implies a faster concentrated response; a broader low peak spreads the volume through time. The area under a discharge hydrograph represents water volume.

Self-check

Can two 100-year floods occur in consecutive years?
Answer
Yes. The recurrence description is probabilistic, not a fixed schedule.
What does hydrograph area represent?
Answer
Time-integrated discharge is water volume.
Why can water weaken a slope?
Answer
Pore pressure can reduce effective stress and frictional resistance, among other effects.

Chapter 38 multiple choice questions

Choose one best answer for each question. Open each answer panel after making your choice.

Under a stationary independent annual model, p = 0.02. What is the chance of at least one exceedance in 10 years?
1. Exactly 2%
2. About 18.3%
3. Exactly 20%
4. About 81.7%
Answer and explanation
B. About 18.3% The chance is 1 − 0.98¹⁰ ≈ 0.183. The complement, about 81.7%, is the chance of no exceedance.
Two discharge hydrographs have equal areas under their curves but different peak heights. What is equal?
1. Peak discharge
2. Time to peak
3. Total water volume over the plotted intervals
4. Maximum water level at every station
Answer and explanation
C. Total water volume over the plotted intervals Discharge integrated through time gives water volume. Equal volumes can be distributed through time differently.
Why can a dry ephemeral channel still be a flood hazard?
1. Dry channels cannot infiltrate any water
2. Its bed must be permanently below sea level
3. Dry conditions prove a flood will occur that day
4. It may carry substantial flow during an event despite being dry between events
Answer and explanation
D. It may carry substantial flow during an event despite being dry between events Ephemeral describes intermittent flow, not absence of flood potential. Event runoff may be concentrated in the channel.
How can rising pore-water pressure promote sliding along a potential failure surface?
1. By reducing effective normal stress and frictional resistance
2. By necessarily increasing grain strength
3. By removing gravity from the slope
4. By turning every rock into clay instantly
Answer and explanation
A. By reducing effective normal stress and frictional resistance Effective stress and frictional resistance can decrease as pore pressure rises. The actual response depends on site conditions.
Which statement correctly interprets a 50-year flood estimate under its statistical assumptions?
1. One flood must occur exactly every 50 years
2. The corresponding annual exceedance probability is 2%
3. A second exceedance is impossible for 49 years
4. The event is guaranteed within every 50-year interval
Answer and explanation
B. The corresponding annual exceedance probability is 2% The conventional annual exceedance probability is 1/50 = 0.02. Recurrence is not a fixed calendar schedule.

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