Foundation Settlement Calculator

Settlement of a shallow foundation on clay is split into three parts with different physics and different time scales. Immediate settlement is elastic distortion at constant volume, estimated here from a modulus and a Poisson ratio of 0.3. Primary consolidation is the volume change that follows dissipation of excess pore water pressure, and it dominates in saturated clay; it is computed from the one-dimensional relation S = (Cc * H / (1 + e0)) * log10((P0 + deltaP) / P0), where H is the thickness of the compressible layer, e0 the initial void ratio, and P0 the existing effective overburden taken at mid-layer. Secondary compression is creep at essentially constant effective stress that continues after the pore pressures are gone. The logarithmic form is used because void ratio plots as a straight line against the logarithm of effective stress once the soil is on the virgin compression line. Stress history decides which stiffness applies. If the preconsolidation pressure Pc exceeds P0 plus the load increment, the soil stays on the much stiffer recompression line and the recompression index Cr governs, typically one fifth to one tenth of Cc; if the final stress passes Pc, the calculation splits into a recompression leg up to Pc and a virgin leg beyond it. Compression index values run about 0.1 to 0.4 for inorganic clays and above 1.0 for organic silts and peat, and Skempton's 1944 correlation Cc close to 0.009 times the liquid limit minus 10 gives a sanity check. Secondary compression is commonly scaled through the ratio of the creep index to Cc, near 0.04 for inorganic clays and 0.05 or more for organic soils. Serviceability limits usually cited are 25 mm total settlement for isolated footings on clay, 50 mm for rafts, and an angular distortion of about 1 in 500 for framed structures. The chief caveats are that the method assumes purely one-dimensional compression with no lateral strain, applies the load increment at a single mid-layer depth instead of a Boussinesq stress distribution, and depends on laboratory values that sample disturbance tends to depress while smearing the break in the curve at Pc.

The quantitative treatment begins with Karl Terzaghi's theory of one-dimensional consolidation, developed at Robert College in Constantinople and published in 1923, which explained why clay foundations keep settling for years after construction. Terzaghi built the oedometer to measure the compression curve directly, and the semi-logarithmic plot of void ratio against effective stress became the standard product of the test, later codified in ASTM D2435. Arthur Casagrande supplied the missing interpretive step at the First International Conference on Soil Mechanics and Foundation Engineering at Harvard in 1936, presenting the graphical construction that locates the preconsolidation pressure from the point of maximum curvature, still the most widely used method for reading stress history from a laboratory curve. The elastic and tolerance sides developed separately. Joseph Boussinesq had published the solution for stresses beneath a point load on an elastic half-space in 1885, which underlies the influence factors used for immediate settlement and for load spreading with depth; John Schmertmann proposed the strain influence factor method for sands in 1970 based on cone penetration data. Tolerable movement criteria came from case histories rather than theory: Arthur Skempton and D. H. MacDonald surveyed 98 buildings in 1956 and related damage to angular distortion, finding cracking around 1 in 300 and structural damage near 1 in 150, and Laurits Bjerrum extended those limits to a range of structure types in 1963. Long-term creep was quantified by Gholamreza Mesri and P. M. Godlewski in 1977, whose constant ratio of secondary compression index to compression index remains the standard way to estimate the tail of the settlement curve.