Overview
This lecture explains how to calculate primary and secondary consolidation settlements in soils using consolidation curves, stress-strain theory, and practical geotechnical engineering methods.
Basics of Consolidation Settlement
- Primary consolidation settlement occurs when a soil layer decreases in height under vertical stress.
- The change in height (ΔH) divided by the original height gives vertical strain.
- Strain = change in void ratio (Δe) / (1 + initial void ratio e₀).
- Settlement (Sₚ) = strain × thickness of soil layer (H).
Using Consolidation Curves
- Consolidation curves provide Δe for a given change in vertical effective stress.
- Δe is determined by calculating the slope (compression index Cc) on the normally consolidated portion of the curve.
- The induced stress is the additional load applied to the soil.
Settlement Calculation Cases
- Case 1 (Normally Consolidated Soil): Initial effective stress ≈ pre-consolidation stress; use Cc from the normally consolidated curve segment.
- Case 2 (Overconsolidated, Remains OC): Initial stress < pre-consolidation stress, and induced stress doesn’t exceed pre-consolidation; use Cr (recompression index).
- Case 3 (OC to NC Transition): Initial stress < pre-consolidation but induced stress exceeds it; use Cr up to pre-consolidation and Cc above it.
- Choose equations based on the stress state before and after loading.
Practical Considerations
- Pre-consolidation stress and over-consolidation ratio (OCR) vary with depth; subdivide soil layers accordingly.
- More sublayers lead to more accurate settlement predictions.
- Use Atterberg limits correlations for Cc and Cr if lab data is unavailable, though lab tests are more reliable.
- Accurate, undisturbed soil samples are critical for reliable pre-consolidation stress measurements.
Homework Example Approach
- Divide soil profile into sublayers where pre-consolidation stress or OCR changes.
- For each sublayer, tabulate depth, thickness, e₀, Cc, Cr, total/effective/induced stress, and pre-consolidation stress.
- Determine case (1/2/3) for each sublayer and calculate settlement accordingly.
- Total settlement is the sum of settlements from all sublayers.
Secondary Consolidation Settlement
- Occurs after primary consolidation due to soil particle degradation.
- Measured from the secondary portion of settlement vs. log(time) curve.
- Settlement = Cα′ × H × log(t₂/t₁), with Cα′ = secondary compression index.
- Time t₁ = time for primary consolidation to end; t₂ = t₁ plus time of interest.
Key Terms & Definitions
- Primary Consolidation Settlement — Decrease in soil volume due to expulsion of water under vertical load.
- Void Ratio (e) — Volume of voids / volume of solids in soil.
- Pre-consolidation Stress (σ′p) — Maximum past effective vertical stress experienced by soil.
- Compression Index (Cc) — Slope of the normally consolidated portion of the consolidation curve.
- Recompression Index (Cr) — Slope of the overconsolidated portion of the consolidation curve.
- Over-consolidation Ratio (OCR) — σ′p / current effective stress.
- Secondary Consolidation Settlement — Additional settlement after primary consolidation due to soil particle compression and chemical changes.
Action Items / Next Steps
- Complete Special Problem #7: Calculate primary consolidation settlement using the recommended sublayer approach.
- Fill out the provided calculation table for each sublayer.
- Use lab or correlated values for Cc and Cr as needed.
- Review example solutions if needed for reference.