K0 is a ratio with a physical boundary condition
Did you know that “at rest” in a marine clay stress report does not mean the seabed is carrying no forces? It means that, in the idealised at-rest earth-pressure condition, lateral deformation is prevented while the soil carries vertical and horizontal stresses. The coefficient K0 is the ratio of horizontal effective stress to vertical effective stress under the relevant zero-lateral-strain state. It is a dimensionless stress ratio, not a force, a friction angle or a universal constant belonging to the mineral alone. A translation that replaces it with “horizontal pressure” loses the definition that makes the quantity useful.
A clay deposit forms under deposition, self-weight, changing pore pressures and possible erosion or unloading. Its vertical effective stress is rarely identical to its horizontal effective stress. Laboratory stress paths that preserve an appropriate horizontal-to-vertical relationship can therefore be more representative of some field histories than an isotropic stress preparation. But reproducing a K0 condition is an experimental and interpretive task, not a routine matter of choosing a pressure. This guide shows how to read the ratio, distinguish effective from total stresses, check sample preparation and interpret stress-path diagrams without treating a conditional parameter as an unqualified site truth.
All worked numbers below are invented educational cases. They are not offshore instrument observations, endorsed design inputs or a substitute for a qualified geotechnical investigation. We will use first principles, dimensional conversions, examples, independent exercises and sources to answer one precise question: what may a report mean when it says marine clay was K0 consolidated, and how can a reader verify that meaning? The goal is to keep the measured channels, the controlled boundary conditions and the analyst’s inference separate.
Why vertical and horizontal stresses differ
Imagine a layer of clay settling beneath progressively deposited sediment. It can compress vertically because there is increasing load above, while neighbouring soil prevents it from freely extending sideways. To remain compatible with the surrounding deposit, the soil develops lateral stress even without a separate horizontal actuator. This is the intuitive origin of an at-rest condition. The vertical and lateral components depend on the material, its deformation history and the current effective-stress state. They need not be equal.
A perfectly isotropic consolidation condition would have equal principal effective stresses, such as 100 kPa vertically and 100 kPa laterally. That gives K0 = 1, but it does not demonstrate that a normally deposited marine clay has an at-rest coefficient of one. An alternative state of 100 kPa vertical and 60 kPa horizontal gives K0 = 0.60. These are different stress paths. If a laboratory says it carried out anisotropic consolidation, the reader should ask whether it specifically maintained zero lateral strain or simply chose unequal stresses for some other reason.
Horizontal effective stress has a direction and a geological meaning. In complicated ground, horizontal stress may vary with orientation, and a single scalar K0 may be insufficient to describe anisotropy. Inclined bedding, tectonic stresses or local disturbance can also change the field picture. The simple vertical–horizontal ratio is a useful starting point for the idealised one-dimensional deposition and consolidation scenario. It should not be read as a guarantee of a complete three-dimensional stress state in an irregular offshore formation.
The effective stress ledger
For a saturated soil in the familiar effective-stress framework, stress acting between grains is obtained by accounting for pore-fluid pressure. In a consistent compression-positive convention, vertical effective stress equals total vertical stress minus pore pressure, and horizontal effective stress equals total horizontal stress minus the corresponding pore pressure. If the same hydrostatic pressure applies at the point, the subtraction must be carried out in both directions before forming K0. The ratio of total horizontal to total vertical stress is generally not K0.
Suppose a fictional reading at one depth has total vertical stress 240 kPa, total horizontal stress 190 kPa and pore pressure 100 kPa. The effective vertical stress is 140 kPa and effective horizontal stress is 90 kPa. Therefore K0 = 90/140 ≈ 0.643. Simply dividing 190 by 240 gives 0.792, a different ratio with a different meaning. The numerical discrepancy is not an obscure technicality: it can materially alter an inferred in-situ stress state and the initial conditions for a laboratory specimen or foundation analysis.
Pressure references must be consistent. A gauge pressure measured relative to atmosphere, an absolute pressure and a hydrostatic pressure referenced to sea level are not interchangeable until their zeros are reconciled. Where offshore pore-water pressure includes the water column above the seabed, ignoring that overburden water in total stress can create contradictions. At a fixed point, effective-stress arithmetic is sound only if all pressure quantities refer to the same physical location, datum and convention. A well-written report includes a stress ledger showing each component and how it was obtained.
A seawater and seabed example with the datum shown
Imagine, for a teaching exercise, 20 m of seawater above the seabed and a measurement point 10 m below the seabed in uniform saturated sediment. Use rounded unit weights of 10 kN/m³ for seawater and 17 kN/m³ for saturated sediment. Total vertical overburden is approximately 20 × 10 + 10 × 17 = 370 kPa. Hydrostatic pore pressure at the point is about 30 × 10 = 300 kPa relative to the same pressure datum. Effective vertical stress is therefore 370 − 300 = 70 kPa.
If the assumed at-rest coefficient is 0.60, horizontal effective stress is 0.60 × 70 = 42 kPa. The corresponding total horizontal stress for this idealised hydrostatic case would be approximately 42 + 300 = 342 kPa. It would be incorrect to multiply the total vertical stress of 370 kPa by 0.60 and call the 222 kPa result the horizontal total stress. The effective ratio was applied to effective vertical stress, not to total stress containing hydrostatic water pressure.
An elegant alternative calculation uses submerged unit weight for the sediment: γ′ = 17 − 10 = 7 kN/m³, so 10 m of uniform soil contributes 70 kPa effective vertical stress. But this shortcut depends on the simplified hydrostatic and unit-weight assumptions, and it does not magically replace a layered ground model. If saline pore fluids, artesian gradients or non-hydrostatic conditions are relevant, calculate the stress and pore-pressure profiles explicitly. The example shows why one should record water depth, seabed datum and pore-pressure reference rather than relying on an unexplained K0 number.
What K0 consolidation attempts to reproduce in a laboratory
In a K0-consolidation stage the laboratory aims to increase or adjust the vertical effective stress while controlling the lateral response so that the specimen experiences essentially zero lateral strain. In an instrumented triaxial or other controlled apparatus, radial stress may be adjusted as axial stress changes. The resulting horizontal-to-vertical stress ratio evolves according to the specimen response under the selected method. The operator measures or infers the appropriate lateral deformation and corrects the stress path to maintain the target condition.
A file that says “anisotropically consolidated at K0 = 0.65” could mean the laboratory actively measured and controlled zero lateral strain, or it could mean it imposed a chosen ratio of 0.65 without directly verifying lateral strain. Those are not exactly the same evidence. A sound technical summary identifies the protocol used, its control quality and the source of the target value. The ratio may be an input to the test or a measured outcome, and it should not be presented as both without explanation.
Apparatus compliance, side drains and membrane effects can cause differences between indicated lateral strain and true specimen deformation. Research on K0 consolidation of undisturbed clays has noted that side drainage arrangements can influence inferred stress ratios. That makes calibration and control-loop documentation important. A label on a graph cannot prove that the underlying specimen spent the entire consolidation stage under zero-lateral-strain conditions. Inspect the actual radial deformation or volume-control record, the stress history and the time over which the target was maintained.
Defining the stress-path axes clearly
Triaxial reports often summarise stresses using mean effective stress p′ and deviator stress q. For a conventional triaxial compression state with one axial effective principal stress σ′a and two equal radial effective principal stresses σ′r, one common convention is p′ = (σ′a + 2σ′r)/3 and q = σ′a − σ′r. Some soil mechanics publications use alternative definitions or factors, so the axes and convention must be stated rather than guessed from a familiar-looking symbol.
Take an invented K0-consolidated stress state with axial effective stress 100 kPa and radial effective stress 60 kPa. The mean effective stress is (100 + 2 × 60)/3 = 220/3 ≈ 73.33 kPa and q = 100 − 60 = 40 kPa. K0 is still 60/100 = 0.60. A plot of q against p′ does not directly show K0 as the slope of every segment unless the mapping and path conditions support that statement. The axes compress two stress components into a useful representation; they do not eliminate the underlying definitions.
Now increase the stresses along a constant ratio path from 100/60 to 150/90 kPa. K0 remains 0.60. The new p′ is (150 + 180)/3 = 110 kPa and q = 60 kPa. Both p′ and q rise. The loading path is anisotropic even though the ratio is held fixed. This exercise makes clear why a curve can move diagonally in q–p′ space during K0 consolidation, unlike an isotropic consolidation line where q is ideally zero.
At-rest pressure is not active or passive earth pressure
Engineers distinguish at-rest, active and passive earth-pressure conditions because they correspond to different deformation states and mobilised responses. At-rest K0 concerns the lateral effective stress when lateral strain is prevented in the idealised condition. Active pressure develops as a retaining boundary moves in a way that allows the soil to unload laterally; passive resistance involves a different displacement and mobilised stress condition. A label such as “K0 pressure” should not be translated as “active earth pressure” merely because both appear in retaining-wall calculations.
For a fictional vertical effective stress of 100 kPa, K0 = 0.60 implies 60 kPa at-rest horizontal effective stress. A different coefficient used for an active calculation would generate a different lateral stress, but it would be wrong to say that value was measured during the original K0 test. The displacement boundary conditions have changed. The larger lesson is that a coefficient belongs to a mechanical state and analysis convention. Copying a number across states without carrying its definition is an error in both engineering and communication.
Similarly, K0 is not a friction angle. Relationships between K0 and effective friction angle sometimes provide approximate estimates under restricted soil-history assumptions. Those correlations do not turn an interpreted K0 into a direct shear-strength measurement. A non-specialist summary should say whether a value came from in-situ measurements, a laboratory stress path, an empirical correlation or an adopted design assumption. The provenance determines how confidently the reader can use the number and what independent checks are necessary.
The Jaky-style approximation and its limits
A widely taught approximate relationship for normally consolidated soils is K0 ≈ 1 − sinφ′, where φ′ is a suitable effective friction angle. For an illustrative φ′ of 30 degrees, sin30° = 0.5 and the expression yields K0 ≈ 0.5. It is an empirical or theoretical approximation under a particular conceptual model, not a direct measurement and not a guarantee for every clay. Soil structure, stress history, anisotropy and choice of relevant friction angle can change the observed relationship.
The same equation would give about 0.577 for φ′ = 25 degrees because sin25° ≈ 0.423. The trend is that the estimated K0 decreases as the assumed friction angle increases over this range. However, a clay that was unloaded from a larger past stress may have an at-rest ratio higher than an otherwise comparable normally consolidated material. An inherited K0 may therefore be more informative when combined with the full stress history than a simple angle-only rule. State when the formula is a screening estimate rather than the chosen final field value.
A real report might contain φ′ values derived from drained strength testing and a K0 value from a separate stress measurement. If they disagree with the approximation, do not silently revise either until they match. Check the tests’ confining stress, drainage conditions, sample fabric and whether the soil was overconsolidated. A correlation is a hypothesis about how quantities may relate, and disagreement can be a useful diagnostic. The best translation preserves the distinction between an approximate model prediction and a measured or interpreted field stress ratio.
Normally consolidated, overconsolidated and unloading paths
Normally consolidated soil has reached its greatest relevant past effective vertical stress under a specified conceptual framework. Overconsolidated soil has experienced a higher relevant stress before subsequent unloading or another history that produces an overconsolidated state. K0 may respond differently during loading and unloading. As the vertical effective stress falls after unloading, the horizontal effective stress does not necessarily decrease proportionally, so the ratio can increase. A K0 above one is therefore not automatically a mathematical impossibility or sensor fault.
Imagine a hypothetical specimen initially at σ′v = 200 kPa and σ′h = 110 kPa, giving K0 = 0.55. After controlled unloading to σ′v = 100 kPa, suppose its horizontal effective stress is still 90 kPa. K0 is then 90/100 = 0.90. The clay has not magically become weaker or stronger by a single amount; the stresses have followed a different path. This numerical exercise demonstrates hysteresis in the ratio without claiming that every clay follows exactly those values.
If an observed K0 is greater than one after unloading, verify both stress components and the pore-pressure reference before rejecting it. A ratio greater than one means horizontal effective stress exceeds vertical effective stress in the chosen orientation, not that a material law was broken. Conversely, an extreme or negative calculated value might indicate sign conventions, transducer offsets or a stress state beyond the simple interpretation. The calculation should be reviewed together with the specimen deformation and its loading history rather than in isolation.
Why stress history can matter more than a tidy constant
Marine sediment accumulates across time, sometimes rapidly, and may experience erosional unloading, seasonal pressure changes or the installation of large structures. The material may be bonded or aged in ways that affect the stress state and deformation response. A single K0 selected from a chart can be useful as a preliminary assumption, but it should not erase the possibility of different histories between layers. A depth profile may require values that vary with geology and effective stress rather than one constant assigned to the entire site.
A natural sediment may also exhibit fabric anisotropy: the arrangement of particles and contacts differs vertically and horizontally because deposition and consolidation have preferred directions. An anisotropically prepared laboratory specimen attempts to better approximate aspects of that in-situ state. But matching the initial stress ratio is not identical to reproducing every aspect of the natural fabric or past shear history. A test may be K0-consolidated yet still require scrutiny for disturbance, stress path and undrained or drained behaviour during the subsequent shearing stage.
Interpretation becomes especially hazardous when a report quotes “K0 strength”. K0 itself is a stress ratio; strength is a different concept. One may use K0 consolidation before a shear test and observe a resulting undrained strength that differs from an isotropically consolidated specimen. The difference may be due to stress anisotropy and fabric, but the K0 ratio should not be renamed as a shear-strength coefficient. Make the test sequence explicit: consolidation stage first, then shearing stage, then the relevant measured or interpreted strength.
What the instrument does not measure by itself
A pressure controller set to a radial pressure does not prove the specimen’s horizontal effective stress equals that display unless pore pressure and apparatus effects are properly accounted for. A volume-change sensor does not necessarily give direct lateral strain without assumptions about shape and drainage. A pressure transducer may have time lag, calibration drift or a pressure reference different from the plotted stresses. The data reduction needs to establish what each channel represents. A competent translation uses verbs such as “applied”, “measured”, “calculated” and “inferred” with care.
At a field site, estimating K0 might involve instruments and indirect correlations distinct from a laboratory triaxial experiment. Overcoring, pressuremeter response, earth pressure cells or geological models can each bring their own limitations. The fact that all report horizontal stress does not guarantee identical definitions or spatial representativeness. Where results conflict, check the method and depth rather than averaging different values as if they were replicates of the same measurement. Measurement provenance is a substantive part of the answer.
A marine soil core may also be disturbed during recovery. The total stress during sampling changes, while the water pressure can change or cavitation may occur. Reconsolidating a disturbed specimen to a selected K0 state does not restore the original particle fabric perfectly. Thus even a carefully controlled laboratory ratio may not prove the pre-sampling in-situ ratio. An honest project narrative acknowledges this when drawing conclusions from relatively small numbers of specimens taken across a variable site.
A fictional vertical stress profile
Let an idealised marine clay layer have submerged unit weight 7 kN/m³. Below a seafloor where the relevant effective vertical stress is approximately zero at the top, the simple hydrostatic effective vertical stress increases by about 7 kPa per metre. At depths 2, 4, 6 and 8 m below seabed, estimated σ′v values would be 14, 28, 42 and 56 kPa. This model assumes uniform soil, no seepage and no exceptional boundary conditions. It is a teaching profile, not a real stratigraphic measurement.
If K0 is assumed constant at 0.65, the corresponding estimated horizontal effective stresses are 9.1, 18.2, 27.3 and 36.4 kPa. These are products of the assumed ratio and the vertical effective stresses. They are not four independent observations of horizontal stress. A plotted line through them may look authoritative, but its certainty cannot exceed the certainty of the soil unit weight and the adopted K0. A credible figure caption would call it an illustrative estimate and explain what field measurements are needed to test it.
Now suppose a thin layer at 6 m has a different stress history and a justified interpreted K0 of 0.85. The horizontal effective stress there would be 0.85 × 42 = 35.7 kPa rather than 27.3 kPa. The local contrast is 8.4 kPa. It would be wrong to smooth that value into the overall 0.65 line if there were reliable evidence of a different state. Yet a single anomalous sensor reading is not enough by itself to prove the layer has a unique stress history. The source of the change and its uncertainty must be documented.
In field design, the stress distribution may also depend on loading from a nearby foundation, sediment erosion or installation-induced pressures. The simple profile should not be carried into these conditions unmodified. It is a starting state for a further analysis, not a prediction of the entire loading trajectory. A good tutorial makes the hand-off visible: establish initial effective stresses, apply appropriate construction and environmental loading, then evaluate changes in pore pressure, strain and strength using the relevant model.
A controlled lab record translated line by line
Consider an invented specimen at the end of an anisotropic consolidation stage. The applied total axial stress is 300 kPa, radial total stress is 230 kPa and measured pore pressure at the relevant reference state is 100 kPa. Then σ′a = 200 kPa and σ′r = 130 kPa, so the effective stress ratio is K = 130/200 = 0.65. If the laboratory maintained essentially zero radial strain, it may describe this as an achieved K0 condition. The ratio alone does not establish the zero-strain condition; the deformation record is the second part of the evidence.
The corresponding p′ is (200 + 2 × 130)/3 = 460/3 ≈ 153.33 kPa and q is 200 − 130 = 70 kPa. This is a stress state with nonzero deviatoric stress before the subsequent shear phase. A chart that calls it “isotropic” is inconsistent with those numbers. Conversely, if a worksheet displays q = 0 at the same stress components, verify whether it used a different convention, imported the wrong column or omitted the pressure corrections. A transparent calculation lets the reader detect the inconsistency.
Suppose the laboratory then performs undrained compression and records rising axial load and changing excess pore pressure. Its inferred effective stress path may depart from the original K0 consolidation line. Calling every subsequent point “K0 stress” would be incorrect unless the lateral strain boundary condition and stress control remain appropriate. The description should separate the end-of-consolidation state from the subsequent shearing response. The latter can be especially relevant to offshore bearing, installation and cyclic response studies, but its interpretation is an additional task.
A reviewer should also ask whether the specimen was loaded toward the in-situ K0 state from below or from above, and whether unloading or reconsolidation occurred. Two samples finishing at the same stress pair can differ in structure or history. A test log that preserves intermediate steps and hold times is more informative than a summary reporting only the final K0. The distinction between end state and path is one of the central lessons of advanced soil mechanics and accurate technical translation.
Errors and the fastest repairs
The first frequent error is using total stresses instead of effective stresses. Recompute both components by subtracting a consistent pore pressure, then form the ratio. The second is reversing numerator and denominator: σ′v/σ′h is the reciprocal of K0. With 100 kPa vertical and 60 kPa horizontal, K0 is 0.60, not 1.67. A reciprocal value may sometimes be used under another named ratio, but it must not be silently relabelled. The third error is mixing kPa and MPa across channels.
Another error is to describe a specified 0.60 target as a measured in-situ value. If the laboratory operator commanded 0.60, the report should say it was imposed and show whether zero lateral strain was actually achieved. Where the coefficient is calculated from the achieved stresses, the distinction shifts toward an inferred laboratory state. Neither automatically proves that the clay at the collection depth had that exact ratio before sampling. A concise annotation of provenance can prevent this mistake.
A fourth error is to carry a normally consolidated correlation into heavily overconsolidated or structured ground without checking stress history. A fifth is to confuse at-rest with active earth pressure, assuming that lateral displacement boundary conditions do not matter. A sixth is to treat a laboratory stress-path symbol p′ or q as if every publication defines it the same way. Each error can be repaired by tracing definitions back to the specific report instead of guessing from superficially familiar notation.
When a measured horizontal stress seems much too large, do not immediately delete it as an outlier. Check sensor zero, hydrostatic correction, confinement, local stress orientation, deformation control and stress history. It may be a genuine overconsolidated state, or it may be an artefact. State the competing explanations and identify what further measurement would resolve them. Publishing a smooth but unexplained profile is less informative than acknowledging the uncertainty at the relevant depth.
Uncertainty and design transfer
Uncertainty in K0 can arise from load-cell calibration, pore-pressure referencing, specimen disturbance, lateral deformation measurements, stress-path control and field geology. Even a small instrument error may affect the ratio when effective stresses are low near the seabed. For example, if horizontal effective stress is 12 kPa and vertical effective stress is 20 kPa, the ratio is 0.60. A ±2 kPa uncertainty in horizontal stress alone already spans roughly 0.50 to 0.70, before uncertainty in the denominator is considered.
A scenario range can make this concrete without implying a particular probability model. Suppose σ′h might be 10–14 kPa and σ′v might be 18–22 kPa. The extreme possible ratio under those independent bounds runs from 10/22 ≈ 0.455 to 14/18 ≈ 0.778. These are bounding combinations, not a confidence interval. The calculation shows how a nominal 0.60 can conceal a wide uncertainty range under low-stress conditions. A proper analysis should use realistic correlations and field constraints rather than assuming independent extremes are equally likely.
A geotechnical model might use K0 to establish the starting stress field for a finite-element analysis or to estimate initial lateral pressure. That model still needs material properties, geometry, loading history, drainage conditions and constitutive assumptions. It does not follow that a structure will be safe because a selected K0 lies within a familiar textbook range. The selection should be justified and, where the consequence is substantial, subjected to sensitivity analysis showing how the predicted response changes under plausible alternative initial stresses.
For a summary intended for non-specialists, it is often enough to say that K0 describes how much horizontal effective stress exists relative to vertical effective stress before significant lateral deformation. But the next sentence should clarify that the ratio depends on stress history and testing method. This two-sentence explanation preserves the idea without pretending that an approximate classroom formula can decide a real offshore design.
Independent transfer problems and answers
Problem one: total vertical stress is 270 kPa, total horizontal stress 200 kPa and pore pressure 120 kPa at the same point. Find K0. Answer: vertical effective stress is 150 kPa and horizontal effective stress is 80 kPa, so K0 = 80/150 = 0.533. Dividing total stresses gives 0.741, which does not satisfy the effective-stress definition. State the pressure datum and assume both total components use the same convention.
Problem two: vertical effective stress is 160 kPa and measured K0 is 0.70. Find horizontal effective stress and p′ and q under the stated triaxial convention. Answer: σ′h = 112 kPa. Then p′ = (160 + 2 × 112)/3 = 384/3 = 128 kPa. The deviator stress is q = 160 − 112 = 48 kPa. Checking the ratio 112/160 returns 0.70. These are derived stress coordinates and should not be reported as separately measured sensors.
Problem three: use the approximate normally consolidated formula K0 ≈ 1 − sinφ′ for φ′ = 30 degrees. Answer: sin30° = 0.5, so the approximate value is 0.50. The correct description is “a correlation-based screening estimate under applicable assumptions”, not “the measured K0 of the sampled clay”. This problem assesses whether a learner can distinguish a calculation from an observation.
Problem four: a field point lies 8 m below seabed in uniform material whose submerged unit weight is 8 kN/m³. With the specified simplified hydrostatic conditions, effective vertical stress is approximately 64 kPa. For assumed K0 = 0.625, horizontal effective stress is 40 kPa. If an analyst instead adds the seawater column to the effective stress without accounting for pore pressure, they have mixed total and effective quantities. The depth reference and water pressure convention must stay explicit.
Problem five: a specimen initially has σ′v = 180 kPa and σ′h = 99 kPa, then is unloaded to 90 kPa vertical while horizontal effective stress remains 81 kPa. Initial K0 is 99/180 = 0.55; final K0 is 81/90 = 0.90. The example demonstrates that the ratio can rise on unloading. It does not prescribe a universal unload–reload law; other materials and stress paths may behave differently.
Frequently asked questions
Is K0 equal to one by definition because the soil is at rest? No. At rest refers to a deformation condition, not isotropic stress. Can K0 exceed one? In some stress histories, especially after unloading, horizontal effective stress can exceed vertical effective stress. Is K0 measured by the same device as CPTu resistance? Not necessarily; a cone and a K0-consolidated laboratory specimen provide different types of information. Does the ratio have units? No. It is one effective stress divided by another with the same units.
Is Jaky’s formula exact for every marine clay? No. It is an approximation whose assumptions and calibration need consideration. Why does pore pressure matter if it is equal in vertical and horizontal directions? Because it is subtracted before forming the ratio; equal subtraction changes the ratio unless the stresses are equal. Does K0 consolidation itself measure undrained shear strength? No; it establishes a stress condition. Strength is assessed through a subsequent loading or shearing stage interpreted with its own conditions.
How should a translator handle unclear K symbols? Preserve the original symbol, give its defined denominator and ask whether it means at-rest, active, passive or another coefficient. What if a report cites K0 = 0.65 but plots 0.60? Check whether 0.65 was the command setpoint and 0.60 the achieved value, whether rounding or stress corrections changed, and whether the two figures refer to the same stage. Do not silently choose one and rewrite the other.
A competent short explanation should let the reader reconstruct the stress pair, understand how it was measured or imposed and see the field assumptions used to interpret it. That is the difference between copying a coefficient and translating its meaning. More words are not inherently better; the useful words are the ones that preserve the physical condition, the numerator and denominator, and the scope of the claim.
Primary research and relevant eduKate reading
For primary methodological context, read Effects of Stress Paths on Undrained Shear Characteristics of Anisotropically Consolidated Cohesive Soil and K0 consolidation of undisturbed clays by means of triaxial cell. The At-Rest Lateral Earth Pressure of Consolidating Clay paper describes the response of a different laboratory configuration through loading and unloading. These are references for scientific reasoning, not the source of the illustrative numbers in this article.
Compare the neighbouring eduKate analysis of CRS consolidation and pore pressure, oedometer stress history and OCR, and direct simple shear under anisotropy. These teach different parts of the same physical chain; none should be substituted for another merely because they use soil stress language.