{"id":1592,"date":"2026-11-02T01:57:28","date_gmt":"2026-11-01T22:57:28","guid":{"rendered":"https:\/\/setaf2018.com\/?p=1592"},"modified":"2026-11-02T01:57:28","modified_gmt":"2026-11-01T22:57:28","slug":"undrained-shear-strength-correlations","status":"publish","type":"post","link":"https:\/\/setaf2018.com\/en\/post\/undrained-shear-strength-correlations\/","title":{"rendered":"Undrained Shear Strength from Correlations: Skempton, Ladd and Kulhawy-Mayne"},"content":{"rendered":"\n

Undrained shear strength, written su or cu, is the shear strength a saturated fine-grained soil mobilises when it is loaded fast enough that no drainage occurs and the water content does not change. It governs short-term stability: a footing on soft clay, an embankment built quickly, an excavation before pore pressures equalise.<\/p>\n\n\n\n

\"Undrained<\/figure>\n\n\n\n

Measuring it requires an undisturbed sample and a laboratory test. Both are expensive, both take time, and sample disturbance degrades the result in a direction that is hard to detect. This is why correlations exist: they estimate undrained strength from index properties and stress history, which are cheaper to obtain and less sensitive to handling.<\/p>\n\n\n\n

A correlation is not a measurement, and the distinction has to survive into the report.<\/p>\n\n\n\n

An undrained strength from a correlation is a statement about clays in general, adjusted for this one. A test is a statement about this one.<\/strong><\/p>\n\n\n\n

What Is Undrained Shear Strength?<\/h2>\n\n\n\n

The shear strength available with the friction angle taken as zero.<\/p>\n\n\n\n

Under undrained conditions the applied load is carried initially by the pore water, so the effective stress does not change and neither does the frictional component of strength. The soil behaves as though it had cohesion only, and the total stress analysis that follows uses su in place of c\u2032 and \u03c6\u2032.<\/p>\n\n\n\n

It is not a fundamental soil property. It depends on the effective stress the soil currently carries, on its stress history, on the direction of shearing and on the rate at which the load is applied. Every correlation in use is an attempt to capture that dependence with the parameters available.<\/p>\n\n\n\n

Why Are Correlations Used at All?<\/h2>\n\n\n\n

Because the direct route is fragile as well as expensive.<\/p>\n\n\n\n

An undisturbed sample is recovered with a thin-walled tube, transported, extruded, trimmed and mounted, and each step disturbs the structure. Disturbance lowers the measured strength, and the effect is systematic rather than random. A poorly sampled stiff clay can test weaker than a well-sampled soft one.<\/p>\n\n\n\n

Correlations bypass that chain by using properties that disturbance does not destroy: plasticity, water content, vertical effective stress and overconsolidation ratio. They carry their own error, but it is a different error, which is why the two routes are used together rather than one instead of the other.<\/p>\n\n\n\n

\"Undisturbed<\/figure>\n\n\n\n

The Normalised Strength Ratio<\/h2>\n\n\n\n

Almost every correlation is expressed as a ratio rather than as a strength.<\/p>\n\n\n\n

The quantity that behaves consistently across clays is su divided by the vertical effective stress at the depth of interest. Strength scales with confining stress, so a normally consolidated clay at twenty metres is stronger than the same clay at two metres in almost exact proportion to the effective stress. Expressing strength as a ratio removes that dependence and leaves the part that varies between soils.<\/p>\n\n\n\n

The practical consequence is that any correlation of this family requires the effective stress profile, which requires the unit weights<\/a> and the groundwater level. An error in either propagates directly into the derived strength.<\/p>\n\n\n\n

Skempton: Strength From Plasticity Index<\/h2>\n\n\n\n

For normally consolidated clays, Skempton (1957) related the normalised strength to plasticity:<\/p>\n\n\n\n

su \/ \u03c3\u2032v = 0.11 + 0.0037 \u00b7 PI<\/strong><\/p>\n\n\n\n

where PI is the plasticity index<\/a> as a percentage.<\/p>\n\n\n\n

The relationship is simple, it uses a property every laboratory measures, and it is widely used for that reason. Its limits are equally clear: it applies to normally consolidated clay, it was derived from a particular set of soils, and it says nothing about overconsolidation. Applied to a stiff overconsolidated clay it underestimates strength substantially.<\/p>\n\n\n\n

Ladd and the SHANSEP Relationship<\/h2>\n\n\n\n

For soils that are not normally consolidated, the stress history has to enter explicitly. Ladd (1991) and the SHANSEP framework express it through the overconsolidation ratio:<\/p>\n\n\n\n

su \/ \u03c3\u2032v = S \u00b7 OCR^( m )<\/strong><\/p>\n\n\n\n

where S is the normalised strength ratio in the normally consolidated state, commonly around 0.22, and m an exponent commonly around 0.8. At OCR = 1 the expression reduces to S, which is the normally consolidated case.<\/p>\n\n\n\n

This form is more demanding than Skempton because it requires OCR, and OCR requires a preconsolidation pressure from an oedometer test. It repays that cost by reproducing the strength of overconsolidated clays, where the plasticity-only relationships fail.<\/p>\n\n\n\n

Kulhawy-Mayne and Related Forms<\/h2>\n\n\n\n

Kulhawy and Mayne (1990) compiled a large database and proposed relationships of the same family, including the widely quoted form with S = 0.22 and m = 0.8, together with correlations for deriving OCR itself from in-situ tests where an oedometer is not available.<\/p>\n\n\n\n

Other expressions in use, including those of Azzouz and of Nagaraj and Murthy, follow the same logic with different parameters and different calibration sets. They are not competing claims about the same soil so much as different summaries of different databases, which is the key to reading them correctly.<\/p>\n\n\n\n

Why Do Two Correlations Disagree on the Same Clay?<\/h2>\n\n\n\n

Because each summarises a different set of soils, and because the strength being predicted is not the same strength.<\/p>\n\n\n\n

The first reason is calibration. A relationship derived from soft marine clays and one derived from glacial tills describe different materials, and neither extrapolates cleanly to the other. Where a soil sits outside the range of the database behind a correlation, the output is an extrapolation with no stated uncertainty.<\/p>\n\n\n\n

The second reason is the mode of shearing, discussed below. A correlation calibrated against triaxial compression tests predicts triaxial compression strength, and a design case controlled by a different shearing mode needs a different value.<\/p>\n\n\n\n

The third is stress history. Skempton with no OCR term and Ladd with one will always diverge on an overconsolidated clay, and the divergence grows with OCR. That is not a disagreement between the two; it is one of them being applied outside its scope.<\/p>\n\n\n\n

Is Undrained Strength a Single Number?<\/h2>\n\n\n\n

No, and treating it as one is the most consequential simplification in the topic.<\/p>\n\n\n\n

Strength depends on how the soil is sheared. In triaxial compression the major principal stress is vertical; in triaxial extension it is horizontal; in direct simple shear the mode is different again. For the same clay, compression typically gives the highest value, extension the lowest, and simple shear between them, with differences that can approach a factor of two in sensitive soils.<\/p>\n\n\n\n

A real design case combines the modes. Along a slip surface beneath an embankment, the soil near the crest is in compression, the soil beneath the toe is in extension, and the soil in between is in simple shear. Using the compression value everywhere overestimates the average available strength.<\/p>\n\n\n\n

Rate matters as well. Undrained strength increases with loading rate, typically by around ten per cent per log cycle of time, so a laboratory test run in hours reports a higher strength than a field loading applied over weeks.<\/p>\n\n\n\n

When Should a Correlation Not Be Used?<\/h2>\n\n\n\n

Where the soil or the application sits outside what the correlation describes.<\/p>\n\n\n\n

Fissured clays behave at mass scale according to the fissures rather than the intact material, and an index-based correlation describes the intact material. Sensitive and quick clays lose a large fraction of their strength on remoulding, and a correlation gives neither the peak nor the remoulded value reliably. Organic soils and peats fall outside the databases entirely. Residual and structured soils derive strength from bonding that index properties do not capture.<\/p>\n\n\n\n

In these materials the correlation is not conservative or unconservative in a predictable direction; it is simply not applicable, and testing is the only route.<\/p>\n\n\n\n

What Does the Divergence Look Like in Numbers?<\/h2>\n\n\n\n

A single worked comparison shows the scale of the issue better than a description of it. Take a clay layer at ten metres depth with a vertical effective stress of 100 kPa and a plasticity index of 30.<\/p>\n\n\n\n

The Skempton relationship gives a normalised strength of 0.11 + 0.0037 \u00b7 30 = 0.221, and therefore an undrained strength of about 22 kPa. The SHANSEP form with S = 0.22 and m = 0.8 gives, at an overconsolidation ratio of 1, a normalised strength of 0.22 and an undrained strength of about 22 kPa as well. At that point the two agree closely, which is expected: both describe the normally consolidated state.<\/p>\n\n\n\n

Now suppose the same layer is lightly overconsolidated, with an overconsolidation ratio of 4. The SHANSEP form gives 0.22 \u00b7 4^( 0.8 ), and since 4 raised to the power 0.8 is approximately 3.03, the normalised strength becomes about 0.67 and the undrained strength about 67 kPa. The Skempton relationship, which carries no stress history term, still returns 22 kPa.<\/p>\n\n\n\n

A factor of three separates the two results, and neither calculation contains an arithmetic error. What separates them is that one of them was applied outside its scope. The same exercise at an overconsolidation ratio of 2 gives a factor of about 1.7, so the divergence is present long before the clay becomes heavily overconsolidated.<\/p>\n\n\n\n

Two correlations that disagree by a factor of three are not evidence that correlations are unreliable. They are evidence that one of them is being asked a question it was not built to answer.<\/strong><\/p>\n\n\n\n

Common Errors in Using Undrained Strength Correlations<\/h2>\n\n\n\n
Error<\/th>Consequence<\/th><\/tr><\/thead>
Skempton applied to an overconsolidated clay<\/td>Strength underestimated, increasingly so with OCR<\/td><\/tr>
Correlation used without the effective stress profile<\/td>The normalising quantity is wrong, so the strength is wrong<\/td><\/tr>
Compression-mode strength applied around a whole slip surface<\/td>Average available strength overestimated<\/td><\/tr>
Correlation applied outside the soil type of its database<\/td>Extrapolation presented as a derived value<\/td><\/tr>
Correlation and laboratory result averaged without reconciling<\/td>Two different quantities combined into one number<\/td><\/tr>
Rate effects ignored for long-duration loading<\/td>Laboratory strength higher than the field mobilises<\/td><\/tr>
Source of the correlation not stated in the report<\/td>Reviewer cannot judge applicability or reproduce the value<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

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

SETAF2018 derives undrained strength from correlations inside the material definition, so the value used in analysis carries the correlation it came from rather than appearing as a typed number.<\/p>\n\n\n\n

The correlation set includes Skempton, Azzouz, Nagaraj\u2013Murthy, Kulhawy\u2013Mayne and Ladd, applied against the effective stress profile built from the borehole layers, unit weights and groundwater conditions in the shared soil profile<\/a>. Because the stress profile and the correlation live in the same model, changing a water level or a layer unit weight updates every derived strength beneath it.<\/p>\n\n\n\n

Where laboratory data exists, the consolidation test is processed in the same model, producing the preconsolidation pressure and the overconsolidation ratio by Casagrande’s construction, which is what the stress-history correlations require. Strength parameters derived this way feed the total stress analyses directly: bearing capacity for foundations<\/a>, the undrained case in slope stability, and the earth pressures used in excavation support.<\/p>\n\n\n\n

Calculation reports<\/a> print the correlation used, the input values and the intermediate steps, so a derived strength can be compared against a laboratory result rather than silently replacing it. The wider laboratory testing<\/a> workflow covers the test data side.<\/p>\n\n\n\n

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

What is undrained shear strength?<\/h3>\n\n\n\n

It is the shear strength a saturated fine-grained soil mobilises when loaded fast enough that no drainage occurs and the water content does not change. It is used in total stress analysis with the friction angle taken as zero, and it governs short-term stability problems.<\/p>\n\n\n\n

Why is undrained strength estimated from correlations?<\/h3>\n\n\n\n

Because measuring it requires an undisturbed sample and a laboratory test, both expensive, and sample disturbance systematically lowers the measured value. Correlations use plasticity, water content, effective stress and stress history, which disturbance does not destroy.<\/p>\n\n\n\n

What is the Skempton relationship?<\/h3>\n\n\n\n

It relates normalised undrained strength to plasticity for normally consolidated clay, as su divided by vertical effective stress equal to 0.11 plus 0.0037 times the plasticity index. It does not account for overconsolidation and underestimates strength in stiff overconsolidated clays.<\/p>\n\n\n\n

What does the SHANSEP relationship add?<\/h3>\n\n\n\n

Stress history. It expresses normalised strength as a normally consolidated ratio multiplied by the overconsolidation ratio raised to an exponent, commonly with values around 0.22 and 0.8. It requires OCR from an oedometer test but reproduces overconsolidated behaviour that plasticity-only forms cannot.<\/p>\n\n\n\n

Why do two correlations give different strengths for the same clay?<\/h3>\n\n\n\n

Because each was calibrated against a different database of soils, because they may predict strength for different modes of shearing, and because one of them may be applied outside its scope, most commonly a normally consolidated relationship used on an overconsolidated clay.<\/p>\n\n\n\n

Is undrained shear strength the same in all directions?<\/h3>\n\n\n\n

No. Triaxial compression typically gives the highest value, triaxial extension the lowest and direct simple shear an intermediate one, with differences approaching a factor of two in sensitive soils. A slip surface combines all three modes, so a single compression value overestimates the average.<\/p>\n\n\n\n

Does loading rate affect undrained strength?<\/h3>\n\n\n\n

Yes. Undrained strength increases with loading rate, commonly by around ten per cent per logarithmic cycle of time. A laboratory test completed in hours therefore reports a higher strength than a field loading applied over weeks or months.<\/p>\n\n\n\n

When should correlations not be used?<\/h3>\n\n\n\n

In fissured clays, where mass behaviour is governed by the fissures rather than the intact material; in sensitive and quick clays; in organic soils and peats; and in residual or structured soils whose strength comes from bonding that index properties do not capture.<\/p>\n\n\n\n\n