Soil State: Void Ratio, Compaction and Consolidation

Three phases, and why void ratio beats porosity

Soil is three materials at once: mineral grains, water, and air. Every index property in geotechnics is a ratio between two of those three, and choosing which ratio to use is not arbitrary.

POROSITY divides the volume of voids by the TOTAL volume. VOID RATIO divides the same voids by the volume of SOLIDS. They describe the same soil and convert into one another, but only one of them has a denominator that stays constant while the soil compresses — the grains do not change volume, and the total does. That is the entire reason void ratio is the working variable in compression and consolidation theory: a change in void ratio is directly a change in volume, with nothing else moving underneath it.

The same logic explains why moisture content is expressed against the DRY mass rather than the wet one, and why dry density rather than bulk density is the compaction control. Referencing everything to the one phase that does not change is what makes the arithmetic of state consistent, and it is why a site measurement that reports bulk density and moisture has to be converted before it can be compared with anything.

Unit weights come out of the same three phases. From a laboratory's dry density, water content and specific gravity, the void ratio is Gs·γw ÷ γd − 1; the moist unit weight puts the pore water back, γd(1 + w); the saturated weight fills every void; and the buoyant weight is the saturated one less water, which is what soil below a water table actually presses with. The degree of saturation, w·Gs ÷ e, doubles as a check on the sheet itself: above one hundred per cent, the three figures did not come from one specimen.

Effective stress: the water carries load and contributes no strength

The stress that matters in soil is not the total weight above a point. It is the part carried by the contacts between grains — the EFFECTIVE stress — which is the total less the pore water pressure. Water transmits pressure equally in all directions and provides no shear resistance, so it holds the grains apart without helping them hold each other.

Every important behaviour follows from that. Strength and stiffness depend on effective stress, so a soil that is strong when drained becomes weak when its pore pressure rises. Lowering a water table INCREASES effective stress across everything beneath it, which is why dewatering settles neighbouring ground that nobody excavated. Raising it does the reverse, which is why a burst main or a blocked drain can cause a failure with no change of load.

It is also why the loading RATE changes the answer in fine soils. Load a clay quickly and the water cannot escape; the pore pressure takes the increment and the effective stress barely moves, so the soil is at its undrained strength. Load it slowly, or wait, and the water drains, the effective stress rises, and the soil gains strength while settling. A clay slope is often at its most vulnerable long after construction, once the pore pressures have equalised — which is the opposite of the intuition that a structure is most at risk on the day it is built.

A compaction percentage is meaningless without its reference test

Ninety-five per cent compaction is not a density. It is a ratio to a maximum dry density obtained in a laboratory test at a specified COMPACTIVE EFFORT, and there is more than one such test.

The two standard efforts differ by roughly a factor of four and a half in energy delivered to the sample. The heavier test produces a higher maximum dry density at a lower optimum moisture content, so ninety-five per cent against it is a materially denser and drier soil than ninety-five per cent against the lighter test. A specification that states a percentage without naming the test has specified nothing, and a field result compared against the wrong curve can pass a soil that fails or fail one that passes.

Moisture is the other half and is often treated as a side condition rather than a requirement. The reference curve has a peak: compacting wet of optimum or dry of optimum both give a lower density for the same effort, and the specification's moisture window exists because effort cannot compensate for water. A soil compacted dry of optimum can also reach the required density and then COLLAPSE on wetting, which is a delayed failure that the passing test result did not predict.

Granular soils need a different reference entirely. A clean sand or gravel does not produce a clear moisture-density peak, so its state is expressed as RELATIVE DENSITY — where it sits between its own loosest and densest achievable void ratios. That is a different scale with different meaning, and quoting a Proctor percentage for a clean granular fill is a category error rather than an approximation.

Consolidation: the site's history matters more than your load

Settlement in a clay is proportional to the logarithm of the RATIO of final to initial effective stress. Because it is a ratio and a logarithm, the same increment of pressure produces far more settlement on a lightly stressed layer near the surface than on a deeply buried one, and doubling a load does not double the settlement.

The dominant variable, though, is what the ground has already been through. Soil remembers the greatest effective stress it has ever carried — its PRECONSOLIDATION pressure — laid down by former overburden since eroded, by an ice sheet, by a previous structure, or by desiccation. Below that level it responds on a recompression path that is typically five to ten times stiffer than its virgin compression path.

So the practical question is not how heavy the new load is but whether the new stress stays below the old maximum. A building that loads a heavily overconsolidated clay within its memory settles modestly and predictably. The same building on a normally consolidated deposit, where every increment is a new maximum, sits on the steep part of the curve. Two identical structures on two sites with similar-looking boreholes can differ by an order of magnitude in settlement for this reason alone.

Time: the drainage path is squared, and it is not the layer thickness

Consolidation is the slow expulsion of water, and the time it takes grows with the SQUARE of the distance that water has to travel to escape. Double the drainage path and the same degree of consolidation takes four times as long.

The path is not the layer thickness. If a compressible layer can drain from both its top and its bottom — sand above and below — the longest journey any water makes is to the nearer face, which is HALF the layer. That halving is squared, so two-way drainage completes in a quarter of the time of the same layer draining one way. Establishing which case applies is therefore worth more than refining any other input, and it is a stratigraphy question rather than a calculation one.

This is also the entire basis of ground improvement by wick drains: they do not make the soil more permeable, they shorten the path. Vertical drains at a metre or two of spacing turn a ten-metre vertical journey into a one-metre horizontal one, and a settlement that would have taken decades occurs during a preload period measured in months.

Primary consolidation is not the end of it. SECONDARY compression continues after the excess pore pressure has dissipated, at a rate roughly constant per logarithmic cycle of time, and in organic soils and peats it can exceed the primary settlement over a structure's life. A prediction that stops at primary consolidation is answering a shorter question than the building asks.

Slopes: water roughly halves the factor of safety

For a long uniform slope in cohesionless soil, the factor of safety is the ratio of the tangent of the friction angle to the tangent of the slope angle — and it contains NO depth term. A dry granular slope is equally stable at one metre and at twenty, which is why such slopes stand at a characteristic angle regardless of their size.

Introduce water and the picture changes sharply. With seepage running parallel to the slope surface and the water table at the surface, the effective unit weight of the soil below it falls to roughly half its saturated weight, and the factor of safety falls by about the same proportion. A slope standing comfortably at a factor of one and a half dry is close to failure fully saturated, with no change in geometry or material.

That is why shallow slope failures arrive with rainfall rather than with loading, why drainage is the first remedial measure considered, and why a temporary cut that stood through a dry summer is not evidence about the following winter. It is also why the infinite-slope result is presented here with its water condition stated on the page: the dry answer and the seeped answer are different enough that reporting one without the other would be misleading.

Swelling clays, and what the laboratory has to settle

Some clays change volume with moisture rather than with load. Smectite-rich soils swell on wetting and shrink on drying, generating pressures well beyond the weight of a light structure, and the resulting movement is seasonal and differential rather than a one-off settlement.

Bentonite is the same mineral used deliberately. In a geosynthetic clay liner the bentonite is meant to hydrate and swell into a low-permeability gel that self-seals around punctures, and the design quantity is its swell rather than its strength. The failure mode is chemical: sodium bentonite's swelling depends on its exchangeable cation, and contact with hard water, seawater or certain leachates exchanges sodium for calcium, after which the material swells far less and the liner's permeability rises. A liner can be installed correctly and lose its function to the water it is holding back.

All of which is why this page ends where it does. Void ratio, compression index, preconsolidation pressure, coefficient of consolidation, friction angle and swell index are LABORATORY measurements — an oedometer, a shear box or triaxial cell, a Proctor mould, a swell index test — and the correlations used to estimate them from a description or a plasticity index carry wide scatter. The calculators here work the arithmetic of state correctly and honestly; the numbers they are given come from a ground investigation, and no arrangement of them can substitute for one.

For foundations near trees, NHBC Chapter 4.2 bands a clay's volume change potential by its MODIFIED plasticity index: the plasticity index times the share of the soil finer than 425 µm (the No. 40 sieve), because the coarser sand and gravel take no part in the swelling. Forty and above is high, twenty to forty medium and ten to twenty low, and a soil counts as shrinkable only with more than 35 per cent fines as well. With the tree's water demand and the ratio of its distance to its mature height, the band is one of the three numbers the chapter's depth charts take.