{"id":1706,"date":"2026-10-02T21:39:32","date_gmt":"2026-10-02T18:39:32","guid":{"rendered":"https:\/\/setaf2018.com\/?p=1706"},"modified":"2026-10-08T14:16:37","modified_gmt":"2026-10-08T11:16:37","slug":"oedometer-consolidation-test","status":"publish","type":"post","link":"https:\/\/setaf2018.com\/en\/post\/oedometer-consolidation-test\/","title":{"rendered":"Oedometer (Consolidation) Test: Casagrande, t50\/t90 and cv"},"content":{"rendered":"\n

The oedometer test, also called the one-dimensional consolidation test, measures how a saturated soil sample compresses under vertical load when lateral strain is prevented and drainage is permitted from the top and bottom faces. It is the source of the parameters used to predict both the magnitude and the rate of consolidation settlement.<\/p>\n\n\n\n

A disc-shaped undisturbed sample is confined in a rigid ring, placed between porous stones, and loaded in increments. Each increment is normally held for 24 hours, with compression recorded by a dial gauge or displacement transducer. Frequent readings during the first hours of selected increments give the rate of compression; the reading at the end of the increment gives its magnitude.<\/p>\n\n\n\n

Two families of result follow, and they answer different questions:<\/p>\n\n\n\n

What is recorded<\/th>Curve produced<\/th>Parameters<\/th>Question answered<\/th><\/tr><\/thead>
Load increments held to completion<\/td>Compression curve<\/td>Cc, Cr, \u03c3\u2032c<\/td>How much settlement<\/td><\/tr>
Readings within one increment<\/td>Time curve<\/td>t\u2085\u2080, t\u2089\u2080, cv<\/td>How fast<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

The oedometer measures one thing directly \u2014 compression under load \u2014 and everything else is obtained by construction on the resulting curves.<\/strong><\/p>\n\n\n\n

What Is Recorded and What Is Derived<\/h2>\n\n\n\n
Stage<\/th>Recorded<\/th><\/tr><\/thead>
Equipment<\/td>Dial gauge multiplier, ring weight, ring height, ring diameter<\/td><\/tr>
Before test<\/td>Specific gravity, ring plus sample weight, sample description<\/td><\/tr>
During test<\/td>Dial readings at 24 hours for each load, rapid readings within selected increments<\/td><\/tr>
After test<\/td>Dry weight of the sample<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

From these, the initial and final state of the sample is established: sample weight and dry weight, natural and dry unit weight, degree of saturation, sample height, equivalent solid height, equivalent void height, equivalent water height, and void ratio.<\/p>\n\n\n\n

The equivalent solid height is the central bookkeeping quantity. It is the height the solid particles would occupy if compressed together with no voids, and it does not change during the test. Every subsequent void ratio is calculated by referencing the current sample height to it, which is why an error in the dry weight or specific gravity propagates through the entire result.<\/p>\n\n\n\n

The Compression Curve<\/h2>\n\n\n\n

Plotting void ratio against the logarithm of effective stress gives the compression curve.<\/p>\n\n\n\n

Its characteristic shape has two branches. At low stresses the sample is being reloaded through stresses it has experienced before, and compression is small \u2014 the recompression branch. Beyond a certain stress the sample begins to experience stresses it has not previously carried, the structure begins to yield, and compression increases markedly \u2014 the virgin compression branch.<\/p>\n\n\n\n

Three parameters are read from the curve:<\/p>\n\n\n\n

Parameter<\/th>Symbol<\/th>Definition<\/th><\/tr><\/thead>
Compression index<\/td>Cc<\/td>Slope of the virgin compression branch<\/td><\/tr>
Recompression index<\/td>Cr<\/td>Slope of the recompression branch<\/td><\/tr>
Preconsolidation pressure<\/td>\u03c3\u2032c<\/td>Stress at the transition between them<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

The preconsolidation pressure is the largest effective stress the soil has carried in its history. Comparing it with the current effective stress gives the overconsolidation ratio:<\/p>\n\n\n\n

OCR = \u03c3\u2032c \/ \u03c3\u2032v<\/strong><\/p>\n\n\n\n

That ratio determines which branch of the consolidation settlement<\/a> equation applies, and therefore whether calculated settlement is measured in millimetres or in tens of millimetres.<\/p>\n\n\n\n

Casagrande\u2019s Construction<\/h2>\n\n\n\n

The transition between the two branches is a curve, not a corner, so \u03c3\u2032c is located by geometric construction. Casagrande\u2019s method is the most widely used.<\/p>\n\n\n\n

  1. Identify the point of minimum radius of curvature on the compression curve.<\/li>
  2. Draw a horizontal line through that point.<\/li>
  3. Draw a tangent to the curve at that point.<\/li>
  4. Bisect the angle between the horizontal and the tangent.<\/li>
  5. Extend the straight virgin compression branch backwards.<\/li>
  6. The intersection of the bisector and the extended virgin branch gives \u03c3\u2032c.<\/li><\/ol>\n\n\n\n

    The first step is the one that decides the answer, and it is made by eye. Two engineers examining the same curve will select slightly different points, and the resulting values of \u03c3\u2032c differ. This is a known and accepted feature of the method rather than a flaw in its application \u2014 but it means that a preconsolidation pressure should be understood as an interpretation of a curve, not a measurement.<\/p>\n\n\n\n

    The load increments chosen affect it as well. A test run over a wide range with few increments defines the transition poorly. Standard load sets covering roughly 25 to 3200 kPa in doubling increments give enough points on both branches for the construction to be made with confidence.<\/p>\n\n\n\n

    Field Correction and the Virgin Curve<\/h2>\n\n\n\n

    The curve obtained in the laboratory is not the curve the soil follows in the field. Sampling, transport, extrusion, and trimming all disturb the specimen, and disturbance flattens the curve: the transition becomes less distinct, the apparent \u03c3\u2032c is lowered, and the measured Cc is reduced.<\/p>\n\n\n\n

    The field compression curve is reconstructed by a further construction, using the in situ void ratio and effective stress at the sampling depth as a fixed point through which the true curve must pass. Extending from that point to a convergence point on the laboratory curve at low void ratio gives corrected field indices, conventionally written Cc* and Cr*.<\/p>\n\n\n\n

    The correction is significant. An uncorrected laboratory Cc can underestimate field compressibility appreciably in a well-structured clay, and the corresponding underestimate of \u03c3\u2032c moves sub-layers from the recompression branch onto the virgin branch \u2014 an error in the conservative direction for settlement, but an error nonetheless.<\/p>\n\n\n\n

    A disturbed sample does not produce a wrong number. It produces a curve that has been flattened, and every parameter read from it inherits that flattening.<\/strong><\/p>\n\n\n\n

    The Rate of Compression<\/h2>\n\n\n\n

    Within a single load increment, the sample does not compress instantly. Excess pore pressure generated by the load must dissipate before the effective stress increases and the soil compresses. The rate at which this occurs is characterised by the coefficient of consolidation:<\/p>\n\n\n\n

    cv = Tv \u00b7 d\u00b2 \/ t<\/strong><\/p>\n\n\n\n

    where d is the drainage path length \u2014 half the sample height, since the oedometer drains from both faces \u2014 and Tv the time factor corresponding to the degree of consolidation reached at time t.<\/p>\n\n\n\n

    Two constructions are used to identify a known degree of consolidation on the measured curve.<\/p>\n\n\n\n

    The Logarithm of Time Method<\/h3>\n\n\n\n

    Compression is plotted against the logarithm of elapsed time. The curve has an initial curved portion, a straight middle portion representing primary consolidation, and a flatter final portion representing secondary compression.<\/p>\n\n\n\n

    The reading corresponding to zero per cent consolidation is found by exploiting the parabolic form of the early part of the curve, comparing readings at times t and 4t. The reading corresponding to one hundred per cent primary consolidation is found at the intersection of the straight primary portion and the tangent to the secondary portion. The reading midway between the two gives fifty per cent consolidation, and the corresponding time is t\u2085\u2080:<\/p>\n\n\n\n

    cv = 0.197 \u00b7 d\u00b2 \/ t\u2085\u2080<\/strong><\/p>\n\n\n\n

    The Square Root of Time Method<\/h3>\n\n\n\n

    Compression is plotted against the square root of elapsed time. The primary portion of this plot is initially linear. A second line is drawn from the same origin with an abscissa 1.15 times that of the first, and its intersection with the measured curve identifies ninety per cent consolidation, giving t\u2089\u2080:<\/p>\n\n\n\n

    cv = 0.848 \u00b7 d\u00b2 \/ t\u2089\u2080<\/strong><\/p>\n\n\n\n

    Why the Two Values Differ<\/h3>\n\n\n\n

    The two methods rarely give the same coefficient, and the difference is not experimental error. Each fits a different portion of the theoretical curve to the measured data, and real soil departs from Terzaghi\u2019s theory in ways that affect the two portions differently \u2014 secondary compression begins before primary consolidation is complete, which distorts the late part of the curve more than the early part.<\/p>\n\n\n\n

    The square root method is generally considered less affected by secondary compression, since it uses data from earlier in the increment. The logarithm method identifies the end of primary consolidation more explicitly.<\/p>\n\n\n\n

    Which value is carried into the time\u2013settlement calculation<\/a> should be a deliberate choice, because it propagates directly into predicted timescales. Reporting both and stating which was used is better practice than reporting one.<\/p>\n\n\n\n

    Stress Dependence<\/h3>\n\n\n\n

    The coefficient of consolidation is not a constant for a soil. It varies with stress level, generally decreasing as the soil is loaded onto the virgin compression branch, because permeability falls faster than compressibility as the void ratio reduces.<\/p>\n\n\n\n

    The value carried into a settlement calculation should therefore come from the load increment that brackets the field stress range, not from an average across all increments. Which increment was used, and why, belongs in the geotechnical report<\/a> alongside the parameter itself.<\/p>\n\n\n\n

    Sources of Error<\/h2>\n\n\n\n
    Source<\/th>Effect<\/th><\/tr><\/thead>
    Sample disturbance<\/td>Flattens the curve; lowers apparent \u03c3\u2032c, reduces Cc<\/td><\/tr>
    Incorrect dry weight or specific gravity<\/td>Propagates through every void ratio in the test<\/td><\/tr>
    Too few load increments<\/td>Transition poorly defined; \u03c3\u2032c construction unreliable<\/td><\/tr>
    Maximum stress below the field stress range<\/td>Virgin branch not adequately defined<\/td><\/tr>
    Sample not fully saturated<\/td>Initial compression includes air voids closing, not consolidation<\/td><\/tr>
    Reading the curvature point carelessly<\/td>\u03c3\u2032c shifted; sub-layers assigned to the wrong branch<\/td><\/tr>
    Averaging cv across increments<\/td>Rate calculated at a stress level the field will not experience<\/td><\/tr>
    Ignoring temperature variation during the test<\/td>Affects the time curve, particularly in long increments<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    Common Errors in Using the Results<\/h2>\n\n\n\n
    Error<\/th>Consequence<\/th><\/tr><\/thead>
    Using laboratory Cc without field correction<\/td>Compressibility underestimated<\/td><\/tr>
    Applying one \u03c3\u2032c across a thick stratum<\/td>Sub-layers assigned to the wrong branch of the settlement equation<\/td><\/tr>
    Using cv from t\u2085\u2080 and t\u2089\u2080 interchangeably<\/td>Predicted timescales differ without acknowledgement<\/td><\/tr>
    Taking cv from an increment outside the field stress range<\/td>Rate prediction based on an inapplicable stress level<\/td><\/tr>
    Reporting \u03c3\u2032c without stating the construction used<\/td>A result that cannot be independently reproduced<\/td><\/tr>
    Ignoring secondary compression in organic or highly plastic soils<\/td>Long-term settlement underestimated<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    Where SETAF2018 Fits<\/h2>\n\n\n\n

    SETAF2018 processes oedometer test data and produces the report directly, rather than requiring the parameters to be derived elsewhere and entered as values.<\/p>\n\n\n\n

    Test definition covers the equipment data, the sample data before and after the test, and the load set, with standard sets available and user-defined sets supported for both the load increments and the rapid reading schedule. Dial readings are entered for each increment, with rapid readings entered against the increments in which they were taken.<\/p>\n\n\n\n

    From that input the software calculates the full state of the sample before and after the test \u2014 weight, dry weight, natural and dry unit weight, degree of saturation, sample height, equivalent solid, void and water heights, void ratio, and the change in void height for each increment \u2014 together with the compression coefficient av and volume compressibility mv.<\/p>\n\n\n\n

    The pressure\u2013void ratio curve is plotted, and Casagrande\u2019s construction is applied from the point of minimum curvature identified on the curve, giving \u03c3\u2032c, Cc and Cr. Entering the in situ effective stress at the sampling depth adds the field curve to the same plot and produces OCR and the corrected field indices Cc* and Cr*. A setting controls whether the curvature point is taken exactly at the selected point, immediately after it, or interpolated between points, which makes the interpretation explicit and repeatable.<\/p>\n\n\n\n

    For the increments with rapid readings, the compression\u2013log t and compression\u2013\u221at curves are plotted, the logarithm and square-root constructions applied to give t\u2085\u2080 and t\u2089\u2080, and both coefficients cv,t50 and cv,t90 calculated. Which one is used in settlement\u2013time analysis<\/a> is selected in the analysis settings rather than fixed.<\/p>\n\n\n\n

    Results are issued as a test report with the tables and curves, saved in a portable format so that a report prepared once can be imported into another project, and the parameters flow into the material definition used by the settlement analysis. The wider laboratory testing<\/a> workflow and the calculation reports<\/a> carry the underlying equations.<\/p>\n\n\n\n

    Frequently Asked Questions<\/h2>\n\n\n\n

    What is an oedometer test?<\/h3>\n\n\n\n

    It is a laboratory test in which a saturated soil sample is confined laterally in a rigid ring and loaded vertically in increments, with drainage permitted from both faces. It measures how much and how quickly the soil compresses, and is the source of the parameters used in consolidation settlement calculation.<\/p>\n\n\n\n

    What parameters does the consolidation test produce?<\/h3>\n\n\n\n

    The compression index Cc, the recompression index Cr, the preconsolidation pressure \u03c3\u2032c and hence the overconsolidation ratio, the coefficient of volume compressibility mv, and the coefficient of consolidation cv.<\/p>\n\n\n\n

    What is Casagrande\u2019s method?<\/h3>\n\n\n\n

    It is the standard geometric construction for locating the preconsolidation pressure on the compression curve, using the point of minimum radius of curvature, a horizontal line, a tangent, their bisector, and the extended virgin compression branch. The intersection of the bisector with the virgin branch gives \u03c3\u2032c.<\/p>\n\n\n\n

    What are t50 and t90?<\/h3>\n\n\n\n

    They are the times at which fifty and ninety per cent of primary consolidation are complete within a load increment, identified from the compression\u2013time curve by the logarithm of time and square root of time constructions respectively. Each gives a coefficient of consolidation through the corresponding time factor.<\/p>\n\n\n\n

    Why do t50 and t90 give different values of cv?<\/h3>\n\n\n\n

    Because each fits a different portion of the theoretical curve to real data, and real soil departs from the theory in ways that affect the two portions differently. Secondary compression, which begins before primary consolidation ends, distorts the later part of the curve more.<\/p>\n\n\n\n

    What is field correction of the compression curve?<\/h3>\n\n\n\n

    It is a construction that reconstructs the compression curve the soil would follow in situ, using the in situ void ratio and effective stress as a fixed point. It corrects for sample disturbance, which flattens the laboratory curve and lowers both the apparent preconsolidation pressure and the measured compression index.<\/p>\n\n\n\n

    How does sample disturbance affect the results?<\/h3>\n\n\n\n

    It flattens the compression curve, making the transition between recompression and virgin branches less distinct, lowering the apparent preconsolidation pressure and reducing the measured compression index. Every parameter read from a disturbed curve inherits that flattening.<\/p>\n\n\n\n

    Is the coefficient of consolidation constant for a soil?<\/h3>\n\n\n\n

    No. It varies with stress level, generally decreasing as the soil is loaded onto the virgin compression branch. The value used in a settlement calculation should come from the load increment bracketing the field stress range.<\/p>\n\n\n\n\n