After this chapter, you should be able to
- Distinguish at-rest, active and passive earth-pressure states.
- Calculate a simple Rankine active resultant.
- Locate triangular and uniform pressure resultants.
- Explain why groundwater and drainage often govern.
- Separate wall checks from global slope and compound stability.
Engineering context and evidenceSource §Lesson 09 · Engineering context and evidence · NHI-06-089 Chapter 10 · NHI-06-088 Chapter 6
Retaining systems work by managing ground movement, water and load paths. Earth-pressure states depend on the direction and magnitude of wall movement; active and passive conditions are not automatic material properties. A stable wall section can still fail through a deep surface that includes the retained ground, foundation or adjacent slope.
Core principles and terminologySource §Lesson 09 · Core principles and terminology · NHI-06-089 Chapter 10 · NHI-06-088 Chapter 6
Soil pressure commonly varies with depth and includes self-weight, surcharge, compaction and water components. Passive resistance requires movement to mobilize and may be lost through excavation, erosion or services. Layering, sloping backfill, interface friction, seismic action and flexible-wall deformation require methods beyond the simple Rankine teaching case.
- At-rest pressure
- Lateral stress state with negligible lateral strain under the adopted ground history.
- Active state
- Lower limiting lateral stress state mobilized by sufficient movement away from retained soil.
- Passive state
- Higher limiting resistance state mobilized by sufficient movement into soil.
- Global stability
- Stability of a failure mechanism extending through the soil mass and potentially around the retaining structure.
Equations, conventions and valid useSource §Lesson 09 · Equations, conventions and valid use · NHI-06-089 Chapter 10 · NHI-06-088 Chapter 6
This form is for a vertical smooth wall, level cohesionless backfill and the Rankine assumptions. Other geometries and interfaces need the governing method.
Paγ acts H/3 above the base for the triangular component; Paq acts H/2 above the base for a uniform surcharge component. Water pressure is a separate action unless drainage is reliably justified.
The resultant elevation follows moment equilibrium about the base for these two components only.
Engineering workflowSource §Lesson 09 · Engineering workflow · NHI-06-089 Chapter 10 · NHI-06-088 Chapter 6
- Define geometry, construction sequence, wall movement compatibility and adjacent assets.
- Develop design strata, drained/undrained strength and credible groundwater states.
- Select at-rest, active, passive or numerical pressure models consistent with deformation.
- Add surcharge, compaction, water and other actions as distinct distributions.
- Check structural resistance, sliding, bearing, eccentricity, uplift and hydraulic failure.
- Check overall, compound and temporary-stage slope stability with applicable methods.
- Specify drainage robustness, monitoring, movement triggers and contingency actions.
| Component | Typical distribution | Control question |
|---|---|---|
| Soil self-weight | Often triangular in simple homogeneous case | Are Rankine assumptions valid? |
| Uniform surcharge | Often uniform lateral increment | Is the load really uniform and remote? |
| Water | Hydrostatic or seepage-dependent | Can drainage be relied upon for design life? |
| Compaction | Construction-induced, method-dependent | Could near-wall pressure exceed the idealized state? |
Verified teaching exampleSource §Lesson 09 · Verified teaching example · NHI-06-089 Chapter 10 · NHI-06-088 Chapter 6
Rankine active resultant with surcharge
For a 4.0 m wall retaining level cohesionless soil, take φ′ = 30°, γ = 18 kN/m3 and uniform surcharge q = 10 kPa. Ignore water and all effects outside the stated Rankine assumptions.
- Coefficient
Ka = tan2(45°−15°)
Ka = 0.3333 - Soil component
Paγ = 0.5×0.3333×18×42
Paγ = 48.00 kN/m - Surcharge component
Paq = 0.3333×10×4
Paq = 13.33 kN/m - Total and line of action
Pa = 61.33; ȳ = (48×4/3 + 13.33×4/2)/61.33
Pa = 61.33 kN/m at 1.478 m above base
Result. The two dry Rankine components total 61.33 kN/m and act 1.478 m above the base. Water and non-Rankine effects must be added separately when relevant.
Rankine active-pressure teaching check
Calculate the two stated dry pressure components and their combined line of action.
- Inputs
- φ′, γ, H and uniform q
- Outputs
- Ka · Soil and surcharge resultants · Total resultant and height above base
- Status states
- Complete teaching case · Invalid or non-finite input · Outside stated method domain
- Validation
- Implemented against the supplied worked example; independent technical approval pending
Rankine Active Pressure Resultant
A dry, vertical, smooth-wall, level, cohesionless-backfill calculation with uniform surcharge.
The two dry components total 61.33 kN/m and act 1.478 m above the base.
- Active coefficient Ka
- 0.3333
- Soil component Paγ
- 48.00 kN/m
- Surcharge component Paq
- 13.33 kN/m
- Total resultant Pa
- 61.33 kN/m
- Height above base
- 1.478 m
Show calculation trail
Ka = tan2(45°−φ′/2) = 0.3333Paγ = 0.5KaγH2 = 48.00 kN/mPaq = KaqH = 13.33 kN/mȳ = Σ(Piyi)/ΣPi = 1.478 m
Failure modes and engineering judgementSource §Lesson 09 · Failure modes and engineering judgement · NHI-06-089 Chapter 10 · NHI-06-088 Chapter 6
- Using active pressure where wall movement is restrained.
- Counting on passive resistance that future excavation could remove.
- Omitting water pressure because drains appear on a drawing.
- Adding force components but using an incorrect resultant height.
- Completing wall sliding and overturning checks without global stability.
Key points
- Earth-pressure state depends on movement and boundary conditions.
- Water should be modelled as a separate credible action unless drainage reliability is demonstrated.
- Force magnitude and line of action both matter.
- Local wall checks do not replace global and temporary-stage stability.
Source references recorded by the supplied chapter
- FHWA NHI-06-089, Soils and Foundations Reference Manual, Volume II, Chapter 10.
- FHWA NHI-06-088, Soils and Foundations Reference Manual, Volume I, Chapter 6.