Terzaghi Consolidation Calculator: Clay Settlement Over Time

simulator intermediate ~12 min
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S = 218 mm — t₉₀ = 5.09 years (double drainage)

A 6 m clay layer with C_c = 0.35 under 100 kPa stress increment settles 218 mm total, reaching 90% consolidation in 5.09 years with double drainage.

Formula

S = C_c · H · log₁₀((σ₀' + Δσ) / σ₀') / (1 + e₀)
T_v = c_v · t / H_dr²
U = 1 − (8/π²) · e^(−π²T_v/4) (for U > 60%)

The Slow Squeeze

When a building or embankment loads saturated clay, the soil doesn't compress instantly. Water trapped in microscopic pores initially carries the entire load as excess pore pressure. Over time — weeks, months, or decades — this water slowly squeezes out through the clay's tortuous pore network. As pore pressure dissipates, the effective stress on the soil skeleton increases and the clay compresses. This process, consolidation, is why buildings on clay can continue settling long after construction ends.

Terzaghi's One-Dimensional Theory

Terzaghi's 1925 consolidation theory models pore pressure dissipation as a diffusion process, governed by the coefficient of consolidation c_v. The dimensionless time factor T_v = c_v·t/H_dr² unifies all consolidation problems: regardless of layer thickness or soil type, the degree of consolidation U depends only on T_v. The simulation plots the isochrones — curves showing pore pressure distribution at different times — as water progressively drains from the clay layer.

Settlement Magnitude

Total primary settlement depends on the compression index C_c, initial void ratio e₀, layer thickness H, and the stress increment Δσ. The logarithmic relationship S = C_cH·log₁₀((σ₀'+Δσ)/σ₀')/(1+e₀) means that doubling the load doesn't double settlement — the response is fundamentally nonlinear. Normally consolidated clays (never previously loaded beyond current stress) settle much more than overconsolidated clays, which have a stiffer initial response governed by the recompression index C_r.

Drainage & Time

Consolidation time scales with the square of the drainage path length H_dr. For double drainage (permeable layers above and below), H_dr = H/2; for single drainage, H_dr = H. This quadratic dependence is why a 1 m laboratory specimen consolidates in minutes while a 10 m field layer takes years. Vertical drains exploit this relationship by reducing the drainage path from the layer thickness to half the drain spacing, potentially accelerating consolidation by orders of magnitude.

FAQ

What is consolidation in geotechnical engineering?

Consolidation is the time-dependent compression of saturated clay soils under sustained loading. When load is applied, pore water pressure increases instantly. As water slowly drains from the clay's tiny pores, effective stress increases and the soil skeleton compresses. This process can take months to decades depending on layer thickness and permeability.

What is the coefficient of consolidation c_v?

c_v is a soil property that controls the rate of consolidation, combining permeability and compressibility into a single parameter with units of m²/year. Typical values range from 0.1 m²/yr for soft organic clays to 10 m²/yr for stiff clays. It is determined from oedometer tests using Casagrande's log-time or Taylor's root-time methods.

What is the difference between single and double drainage?

Single drainage means water can escape from only one face of the clay layer (e.g., clay underlain by impermeable rock). Double drainage allows water to escape from both top and bottom (e.g., clay between sand layers). Double drainage halves the drainage path, reducing consolidation time by a factor of four since time scales with H_dr².

How do you speed up consolidation?

Prefabricated vertical drains (PVDs or wick drains) installed in a grid pattern shorten the drainage path from the layer thickness to half the drain spacing (typically 1-2 m). Combined with surcharge preloading, this technique can achieve years of settlement in months, enabling construction on soft ground that would otherwise be unbuildable.

Sources

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