Consolidation Settlement Calculator (Terzaghi)
Find the primary consolidation settlement and time for 90% consolidation of a normally consolidated clay layer using Terzaghi's one-dimensional consolidation theory.
🪨 What is Consolidation Settlement?
Consolidation settlement is the gradual downward movement of the ground surface that occurs as a saturated clay layer slowly compresses under an applied load, driven by pore water being squeezed out and expelled from the soil over time. Terzaghi's one-dimensional consolidation theory, developed in the 1920s, remains the standard method for predicting both how much a normally consolidated clay layer will ultimately settle and how quickly that settlement will happen.
Geotechnical engineers run this calculation whenever a structure's foundation load will be carried, even partly, through a clay layer. A structural engineer designing a footing on soft ground checks predicted settlement against the structure's tolerance for differential movement before finalizing the foundation type. A highway engineer building an embankment over a clay deposit uses the time-for-90%-consolidation result to plan a staged construction schedule or decide whether ground improvement (like wick drains) is needed to speed up the timeline. A geotechnical consultant reviewing a proposed building site compares settlement predictions across several clay layer thicknesses to flag where deep foundations might be needed instead of shallow footings.
A common misconception is that consolidation settlement happens instantly once a load is applied. In reality, it can take months, years, or even decades to complete, since it depends on how quickly excess pore water pressure can dissipate through the clay, a process governed by the coefficient of consolidation Cv and the drainage path length, not by the load itself. This is different from immediate (elastic) settlement, which does happen essentially instantly as the load is applied.
This calculator takes the clay's compression index, initial void ratio, layer thickness, initial effective stress, stress increase, coefficient of consolidation, and drainage condition, and returns the primary consolidation settlement, the time for 90% of that settlement to occur, and a chart showing how settlement changes as the applied stress increase changes.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Medium Clay Layer, Single Drainage
Cc = 0.3, e0 = 0.8, H = 3 m, σ'0 = 100 kPa, Δσ = 50 kPa, Cv = 2 m²/yr, single drainage
Example 2 — Soft Thick Clay, Double Drainage
Cc = 0.25, e0 = 1.0, H = 4 m, σ'0 = 80 kPa, Δσ = 120 kPa, Cv = 1.5 m²/yr, double drainage
Example 3 — Stiffer Clay Under a Light Load
Cc = 0.4, e0 = 1.2, H = 2.5 m, σ'0 = 60 kPa, Δσ = 40 kPa, Cv = 3 m²/yr, single drainage
❓ Frequently Asked Questions
🔗 Related Calculators
What is Terzaghi's consolidation theory?
Terzaghi's one-dimensional consolidation theory, developed in the 1920s, describes how a saturated clay layer settles over time as an applied stress gradually squeezes pore water out and transfers load from the water onto the soil skeleton. It predicts both the final (primary) settlement magnitude and the rate at which that settlement occurs.
How do you calculate primary consolidation settlement?
For normally consolidated clay, Sc = (Cc times H divided by (1 plus e0)) times log base 10 of ((sigma0 plus Delta-sigma) divided by sigma0), where Cc is the compression index, H is the clay layer thickness, e0 is the initial void ratio, sigma0 is the initial effective overburden stress, and Delta-sigma is the stress increase from the applied load.
What is the difference between normally consolidated and overconsolidated clay?
Normally consolidated clay is currently under the highest effective stress it has ever experienced in its geologic history. Overconsolidated clay was once under a higher stress (from since-removed glacial ice, eroded soil, or a past structure) and has since been unloaded, so it settles far less under the same new stress increase, using the recompression index Cr instead of Cc, a case not covered by this calculator.
How do you find the time for 90% consolidation?
t90 = T90 times Hdr squared divided by Cv, where T90 = 0.848 is the standard time factor for 90% degree of consolidation, Hdr is the drainage path length, and Cv is the coefficient of consolidation. Hdr equals the full clay layer thickness H for single drainage (one permeable boundary) or H divided by 2 for double drainage (permeable boundaries on both sides).
What is the coefficient of consolidation Cv?
Cv is a soil property that governs how fast excess pore water pressure dissipates during consolidation, typically measured in a laboratory oedometer test and expressed in square meters per year. Typical values range from about 0.5 to 5 m2/year for clays, with stiffer, more permeable clays consolidating faster (higher Cv) than soft, highly plastic clays.
Why does drainage condition matter so much for consolidation time?
Drainage condition sets the drainage path length Hdr, the longest distance a water particle must travel to escape the clay layer. Since t90 is proportional to Hdr squared, halving Hdr (going from single to double drainage) cuts the consolidation time to one quarter, a much larger effect than a simple halving.
What is the initial void ratio e0 and how do I estimate it?
The void ratio e0 is the ratio of void (water and air) volume to solid particle volume in the undisturbed clay before any additional load is applied. It is normally obtained from a laboratory index test, but 0.5 to 0.8 is a reasonable planning estimate for a medium-stiff clay, while soft, high-plasticity clays can exceed 1.0 to 1.5.
Does a higher initial effective stress sigma0 increase or decrease settlement?
A higher initial effective stress sigma0 decreases settlement for the same stress increase Delta-sigma, because the stress ratio (sigma0 plus Delta-sigma) divided by sigma0 gets closer to 1 as sigma0 grows, shrinking the logarithm term. This is why a deeply buried clay layer under high overburden pressure settles less than a shallow layer under the same applied load increase.
Can this calculator be used for sand or other non-clay soils?
No. Terzaghi's consolidation theory applies specifically to saturated fine-grained soils like clay and silt, where settlement is controlled by the slow dissipation of excess pore water pressure. Sand drains quickly and settles almost immediately under load, a different mechanism (immediate or elastic settlement) not modeled by this consolidation formula.
Why is settlement plotted against a logarithmic curve instead of a straight line?
The consolidation settlement formula includes a log base 10 term on the stress ratio, so settlement grows more slowly at higher stress increases than at lower ones for the same size step. The chart on this page shows this directly, the settlement-versus-stress-increase curve rises steeply at first, then flattens as Delta-sigma grows larger.