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DSE Geography | Mass Movement and Slope Safety Lesson-Prep Guide (Tutor Edition) | Safety Factor, Rainfall Effect and Stabilisation
Students can say landslides are dangerous, yet cannot say why the same slope fails after rain. This lesson turns stability into one number they can compute.
Objectives — Students can: (1) compute a factor of safety from cohesion, friction angle and slope angle and judge whether a slope is stable; (2) explain how infiltration cuts the factor of safety from 0.844 to 0.693 through pore water pressure; (3) compare regrading, drainage, soil nails and retaining walls, and say why works must lift the factor above 1.5.
01 Prerequisites (3-minute check)
If any of these fails, fix it before the lesson starts.
| Skill | Quick check | Pass mark |
|---|---|---|
| Components of weight | Which two directions does weight split into on a slope | Down-slope and into the slope |
| Stress units | How many kN per square metre is one kPa | 1 kPa = 1 kN/m2 |
| Percentage change | From 0.844 down to 0.693 is a fall of how much | 0.151, about 17.9% |
02 Lesson flow (60 minutes)
| Time | Stage | Tutor does | Student does |
|---|---|---|---|
| 0-10 min | Four slide types | Fall, slide, flow and creep, each with a local scene | One field clue each |
| 10-22 min | Shear balance | Driving force against resisting force | Write 0.844 |
| 22-34 min | Rainfall effect | Pore pressure rises, effective stress falls | Write 0.693 |
| 34-44 min | Ranking the triggers | Storm rain, cutting, fill, vegetation clearing, blocked drains | Order all five |
| 44-54 min | Stabilisation works | Regrade, drain, nail, wall | Compute 960 kN |
| 54-60 min | Exit check | Three questions marked on the spot | All three right |
03 Teaching script (read it out)
Scene 1: Stability is a division: resistance over driving force
On a 45-degree slope with 5 m of soil at 18 kN per cubic metre, the driving stress is 18 x 5 x sin45 x cos45 = 45 kPa.
The resisting stress is cohesion 12 plus effective normal stress 45 x tan30 = 12 + 25.98 = 37.98 kPa.
The factor of safety is 37.98 / 45 = 0.844. Below 1 means resistance has lost and the slope moves; engineering practice asks for 1.5 or more, meaning resistance must exceed driving stress by half.
Stability is therefore not a feeling but a division: raise the numerator or lower the denominator.
The resisting stress is cohesion 12 plus effective normal stress 45 x tan30 = 12 + 25.98 = 37.98 kPa.
The factor of safety is 37.98 / 45 = 0.844. Below 1 means resistance has lost and the slope moves; engineering practice asks for 1.5 or more, meaning resistance must exceed driving stress by half.
Stability is therefore not a feeling but a division: raise the numerator or lower the denominator.
Ask students: what does a factor above 1 mean, and why does practice demand 1.5 rather than 1.
Scene 2: Rain does not add weight, it removes support
After a storm the water table rises 1.2 m, so pore pressure is 9.81 x 1.2 = 11.8 kPa. Water pushes the grains apart, effective normal stress falls from 45 to 33.2 and resistance drops to 12 + 19.17 = 31.17 kPa.
The factor of safety falls from 0.844 to 0.693, a drop of 17.9%. Weight barely changed; what changed is how hard the grains still press on each other.
Monitoring must therefore watch rainfall and groundwater, not only steepness: the same slope is safe in dry weather and fails in a storm.
The factor of safety falls from 0.844 to 0.693, a drop of 17.9%. Weight barely changed; what changed is how hard the grains still press on each other.
Monitoring must therefore watch rainfall and groundwater, not only steepness: the same slope is safe in dry weather and fails in a storm.
Ask students: what happens to the force pressing grains together once water enters the pores (water shares it, so effective stress falls).
Scene 3: Works buy a factor, they do not remove risk
Regrading from 45 to 30 degrees cuts driving stress to 38.97 kPa; adding soil nails to raise cohesion to 25 kPa gives resistance of 63.97 kPa and a factor of 1.64, just acceptable.
For a retaining wall, the active earth pressure coefficient is (1 – sin30)/(1 + sin30) = 0.333, so base pressure is 0.333 x 18 x 4 = 24 kPa. A wall 20 m long and 4 m high carries 0.5 x 24 x 4 x 20 = 960 kN, roughly 98 tonnes.
Drainage is cheapest but treats the trigger, not the angle; nails need drilling and grouting; a wall saves land but must pass 960 kN into the ground. A rock falling 30 m arrives at 24.3 m per second, so the toe of a slope needs a clear buffer, never housing.
For a retaining wall, the active earth pressure coefficient is (1 – sin30)/(1 + sin30) = 0.333, so base pressure is 0.333 x 18 x 4 = 24 kPa. A wall 20 m long and 4 m high carries 0.5 x 24 x 4 x 20 = 960 kN, roughly 98 tonnes.
Drainage is cheapest but treats the trigger, not the angle; nails need drilling and grouting; a wall saves land but must pass 960 kN into the ground. A rock falling 30 m arrives at 24.3 m per second, so the toe of a slope needs a clear buffer, never housing.
Ask students: which term in the formula does each of the four methods change (cohesion, driving stress or pore pressure).
04 Question types and worked steps
| Type | Example | Steps | Answer |
|---|---|---|---|
| Calculation | Factor of safety | Driving stress first, then cohesion plus effective normal times tan phi | 0.844 |
| Calculation | Factor after rain | Pore pressure is unit weight of water times rise; effective stress is driving minus pore pressure | 0.693, down 17.9% |
| Calculation | Wall thrust | Coefficient from phi, base pressure, then half base times height times length | 960 kN |
| Explanation | Why one slope fails only after rain | Infiltration, pore pressure, effective stress, resistance | Compare both factors |
Sanity check (teach this): A factor of safety divides two stresses, so the units must match: kPa over kPa.
Pore pressure lowers effective normal stress only; it cannot change the driving stress because weight is unchanged.
The friction term uses effective stress, never total stress; forget to subtract pore pressure and the wet-weather drop never appears.
Cohesion is in kPa and cannot be added to a force in kN; only the wall thrust is a force.
A factor of safety cannot be negative; a negative effective stress means the soil has liquefied, which is a different failure mode.
Pore pressure lowers effective normal stress only; it cannot change the driving stress because weight is unchanged.
The friction term uses effective stress, never total stress; forget to subtract pore pressure and the wet-weather drop never appears.
Cohesion is in kPa and cannot be added to a force in kN; only the wall thrust is a force.
A factor of safety cannot be negative; a negative effective stress means the soil has liquefied, which is a different failure mode.
05 Independent practice (3 questions)
| Question | Answer | What to watch |
|---|---|---|
| Factor for a 45-degree slope, 5 m, cohesion 12, phi 30 | 0.844 | Driving 45, resisting 37.98 |
| Factor after the water table rises 1.2 m | 0.693 | Pore pressure 11.8, resisting 31.17 |
| Thrust on a 20 m long, 4 m high wall | 960 kN | Coefficient 0.333, base pressure 24 kPa |
06 Common mistakes and what to say
| Mistake | Student writes | Say this |
|---|---|---|
| Treating rain as extra weight | Answering that wet soil is heavier so it fails | Weight barely moves; water pressure separates the grains and effective stress falls. |
| Forgetting pore pressure | Using total stress 45 in the friction term | The friction term needs effective stress, so subtract pore pressure first. |
| Calling 0.84 safe | Answering that 0.84 is close to 1 and therefore stable | Below 1 resistance has lost, so the slope moves. |
| Trusting a wall forever | Answering that a wall ends the risk | A wall needs drainage; trapped water pressure pushes it over. |
07 Homework (paper, section and question numbers)
- Secondary geography chapter index — All chapters and practice
- All lesson-prep guides — Compare other subjects
08 Exit check (last 5 minutes)
| Question | Answer | Decision |
|---|---|---|
| Factor on the 45-degree slope | 0.844 | All three right: move to industry and cities |
| Factor after rain and its drop | 0.693, down 17.9% | One wrong: reteach effective stress |
| Wall thrust | 960 kN | Two wrong: return to act three |
09 Tutor FAQ
Must students memorise every slope number in Hong Kong?
No. Papers supply data; the skill is judging stability and choosing works.
Is a higher factor always better?
It is safer but costs rise steeply; practice settles on 1.5, and more is public money wasted.
Why is drainage usually first?
It changes the trigger, water pressure, at the lowest cost and restores safety at once.
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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.
