7.2 Consolidation, Compaction, and Settlement
Key Takeaways
- Compaction is a construction density process; consolidation is time-dependent volume loss as excess pore pressure drains from saturated fine-grained soil.
- Compaction acceptance compares field DRY unit weight to the Proctor maximum dry unit weight, so wet density must be converted first.
- Primary consolidation settlement uses Sc = (Cc H)/(1+e0) x log10(sigma_f'/sigma_0') and depends on effective stress change, not surface load alone.
- Overconsolidated clay recompresses on a flatter Cr curve until the preconsolidation pressure is exceeded.
- WRE settlement threatens serviceability of clarifiers, tanks, pump buildings, levees, basins, and buried gravity sewers long before strength failure.
Construction Density Versus Long-Term Compression
Water projects place embankments, bury pipes, support treatment tanks, excavate pump stations, and build basins. These features can fail serviceability long before they fail strength if soil settles, softens, or is placed at the wrong moisture-density state. The exam separates three ideas:
- Compaction: a field process that uses mechanical effort (rollers, plates, rammers) to densify soil by expelling air and rearranging particles.
- Consolidation: time-dependent volume reduction in saturated fine-grained soil as excess pore water pressure dissipates and effective stress rises.
- Settlement: the observed vertical movement, from immediate elastic distortion, primary consolidation, secondary compression (creep), collapse of loose fill, or poor placement.
Compaction Checks
Most compaction items hinge on dry unit weight. If the field test reports moist (wet) unit weight and water content w, convert before comparing to the spec:
- Dry unit weight: gamma_d = gamma_moist / (1 + w), with w as a decimal.
- Relative compaction: RC = gamma_d(field) / gamma_d(max, Proctor) x 100%.
Standard Proctor (ASTM D698) and modified Proctor (ASTM D1557) give different maximum dry densities; modified effort yields a higher gamma_d,max at a lower optimum moisture, so never mix the two references in one problem.
| Data item | Meaning | Exam use |
|---|---|---|
| Maximum dry unit weight | Peak of the Proctor curve | Denominator for percent compaction |
| Optimum moisture content | Water content at gamma_d,max | Field moisture target, not a pass guarantee |
| Field wet density | Includes water mass | Must be converted to dry density |
| Relative compaction | Field dry vs lab maximum | Acceptance check (often 90% or 95%) |
Clay is moisture-sensitive: too dry forms clods that will not knit; too wet pumps, ruts, and loses strength. Granular pipe bedding leans on gradation, lift thickness, and method, but a specified compaction percentage still uses the dry-density basis.
Consolidation Settlement
For a normally consolidated clay layer the one-dimensional primary settlement is:
Sc = (Cc x H)/(1 + e0) x log10(sigma_f' / sigma_0')
where Cc is the compression index, H the layer thickness, e0 the initial void ratio, and sigma_0', sigma_f' the initial and final effective vertical stresses at mid-layer. The setup beats memorization: use effective stress, apply the stress increase at the clay depth (not the ground surface), and respect stress history.
Overconsolidated clay recompresses along the flatter recompression index Cr until the preconsolidation pressure sigma_p' is exceeded; only beyond sigma_p' does the full Cc curve apply. If a problem gives sigma_p', compare it to sigma_f' before choosing the relationship. Time-rate items use the coefficient of consolidation cv, drainage path length, and degree of consolidation U, but many WRE items stop at settlement magnitude.
WRE Settlement Risks
A clarifier, storage tank, or pump building tolerates limited differential settlement because piping, weirs, equipment, and slabs need alignment. A levee or basin embankment can lose freeboard. A buried gravity sewer can lose its design slope if trench backfill is poorly compacted, reversing flow. A force main tolerates grade change hydraulically but its joints and thrust blocks can still be damaged.
Workflow:
- Classify the mechanism: compaction, immediate, primary consolidation, or secondary.
- Convert wet density to dry density before any compaction comparison.
- Find the effective-stress increase at the soil layer, not just the surface surcharge.
- Use effective stress for consolidation in saturated soils.
- Check normally consolidated versus overconsolidated against sigma_p'.
- Translate the result into the WRE consequence: pipe slope, tank levelness, or freeboard.
Worked Example: Embankment Over Soft Clay
Suppose a 4 ft compacted fill (gamma = 125 pcf) is placed over a 10 ft normally consolidated clay (e0 = 1.0, Cc = 0.30) whose mid-depth initial effective stress is 1,200 psf. The added stress at mid-clay from the fill is roughly 4 x 125 = 500 psf (ignoring stress spreading for a quick check), so sigma_f' = 1,200 + 500 = 1,700 psf. Then:
Sc = (0.30 x 10)/(1 + 1.0) x log10(1700/1200) = 1.5 x log10(1.417) = 1.5 x 0.1513 = 0.227 ft, about 2.7 inches.
If instead the clay were overconsolidated with sigma_p' = 1,900 psf, the full load stays below sigma_p', so settlement would follow the much flatter recompression index Cr (often 0.1 to 0.2 of Cc), giving only a fraction of an inch. Always test sigma_f' against sigma_p' before choosing Cc or Cr.
Secondary Compression and Differential Movement
After primary consolidation ends, secondary compression (creep) continues at the rate Ss = Calpha x H / (1 + ep) x log10(t2/t1), where Calpha is the secondary compression index and ep the void ratio at the end of primary. It matters for organic soils and peats under levees and lagoons. For most inorganic WRE clays it is small relative to primary settlement.
Differential settlement, not total settlement, usually controls serviceability. A pump building can survive 2 inches of uniform settlement but crack at 0.75 inch of differential across 20 ft. Quick comparison:
| Mechanism | Driven by | Time scale | Typical WRE concern |
|---|---|---|---|
| Immediate (elastic) | Load on stiff or granular soil | Instant | Tank pad on sand |
| Primary consolidation | Pore-pressure drainage in clay | Months to years | Basin over soft clay |
| Secondary compression | Creep after primary | Years to decades | Levee on peat |
| Collapse | Wetting of loose fill | Sudden | Poorly placed backfill |
Exam Strategy
When answer choices mix density and settlement language, separate them. A fill can pass compaction yet still load an underlying soft clay enough to consolidate for years. Conversely, a perfect consolidation calculation does not rescue trench backfill that was accepted by comparing wet density directly to Proctor dry density. If the prompt names a tank, clarifier, or buried gravity pipe, ask whether differential movement, not just magnitude, drives the right answer.
A trench backfill field test reports a moist unit weight of 124 pcf at a water content of 12 percent. The standard Proctor maximum dry unit weight is 115 pcf. What is the relative compaction?
A normally consolidated clay layer is 8 ft thick with e0 = 0.90 and Cc = 0.25. The average effective vertical stress increases from 1,500 psf to 2,300 psf under a proposed basin embankment. What primary consolidation settlement is closest?