Consolidation
When a saturated clay is loaded, it cannot compress immediately, because water fills the pores and water is nearly incompressible. At first the load is carried by excess pore water pressure. Water then slowly squeezes out, the pressure dissipates, the load transfers to the soil skeleton and the clay compresses. This time-dependent compression is consolidation. In sands it happens almost at once; in thick clays it can take years or decades, which is why buildings and embankments on soft clay keep settling long after construction.
Two questions matter: how much, and how fast. The magnitude comes from the oedometer test, which gives the relationship between void ratio and the log of effective stress. A normally consolidated clay, never loaded beyond its present stress, follows the virgin line with compression index Cc. An overconsolidated clay, once loaded more heavily, is much stiffer until the preconsolidation pressure is exceeded. Settlement of a layer is its thickness times the change in void ratio over one plus the initial void ratio.
Rate comes from Terzaghi's one-dimensional theory: degree of consolidation depends on the time factor Tv = cv t / H², where H is the longest drainage path. Doubling the drainage path quadruples the time. That is why vertical drains are installed in soft ground to shorten drainage paths, often with a surcharge to speed settlement before construction. Secondary compression, a slow creep after pore pressure dissipates, matters in organic clays and peat.
NC clay: S = Cc H / (1 + e₀) × log₁₀(σ′f / σ′₀)mv form: S = mv Δσ′ HTime factor: Tv = cv t / H_dr²For U < 60 percent: Tv ≈ (π/4) U²; U = 90 percent at Tv = 0.848
- Terzaghi's theory assumes one-dimensional drainage and compression, saturated soil, constant cv and mv, and small strains.
- Using the stress at mid-depth for the whole layer is acceptable for thin layers; divide thick layers into sub-layers.
- Overconsolidated clays need Cr up to the preconsolidation pressure; secondary compression is extra.
Problem. A 4 m normally consolidated clay layer, drained top and bottom, has e₀ = 1.1, Cc = 0.32 and cv = 2 m²/year. Effective stress at mid-depth rises from 60 to 100 kPa. Find final settlement and time for 90 percent consolidation.
- S = 0.32 × 4 / 2.1 × log₁₀(100/60) = 0.6095 × 0.2218 = 0.135 m.
- Double drainage: H_dr = 2 m.
- t90 = 0.848 × 2² / 2 = 1.70 years.
- So about 135 mm settlement, with 90 percent reached in about 1.7 years.
Answer. About 135 mm; about 1.7 years to 90 percent
Quick quiz
1Why is consolidation of clay slow?
Water must flow out through tiny pores of low permeability.
2What happens to time if drainage path doubles?
Time increases four times.
3Name a method to speed up consolidation.
Vertical (prefabricated) drains, often with surcharge.
- IS 2720 (series) (India): Methods of test for soils: water content, limits, compaction, shear and others, each in its own part.
- IS 1498 (India): Classification and identification of soils for general engineering purposes.
Clauses and documents to read
- IS 2720 (Part 15):1986 (consolidation properties)
- IS 8009 (Part 1):1976 (settlement of shallow foundations)
Cited by number and clause only. We do not reproduce clause text, tables or figures (BIS Act 2016, s.10(5) and s.11). Check the current edition and amendments before use.
References and further reading
Standard texts, listed in no order of merit. We do not copy text, figures, tables or solved problems from any book; our explanations and examples are original.
- Gopal Ranjan, A. S. R. Rao, Basic and Applied Soil Mechanics, New Age International, latest edition.
- B. M. Das, Principles of Geotechnical Engineering, Cengage, latest edition.
- K. Terzaghi, R. B. Peck, G. Mesri, Soil Mechanics in Engineering Practice, Wiley, 3rd edition.
- J. A. Knappett, R. F. Craig, Craig's Soil Mechanics, CRC Press, latest edition.
Free and official sources
Found an error? Write to indiacongroupofengineers [at] gmail [dot] com. For corrections and feedback. We never ask for payment or personal details.