Consolidation (soil)

Last updated May 14, 2019

Two oedometers at the University of Cambridge Oedometer.jpg — Two oedometers at the University of Cambridge

In. soil mechanics, consolidation refers to the process by which soil changes volume gradually in response to a change in pressure. This happens because soil is a two-phase material, comprising soil grains and pore fluid, usually groundwater. When soil saturated with water is subject to an increase in pressure, the high volumetric stiffness of water compared to the soil matrix means that the water initially absorbs all the change in pressure without changing volume, creating excess pore water pressure. As water diffuses away from regions of high pressure due to seepage, the soil matrix gradually takes up the pressure change and shrinks in volume. The theoretical framework of consolidation is therefore closely related to the diffusion equation, the concept of effective stress, and hydraulic conductivity.

Soil mechanics is a branch of soil physics and applied mechanics that describes the behavior of soils. It differs from fluid mechanics and solid mechanics in the sense that soils consist of a heterogeneous mixture of fluids and particles but soil may also contain organic solids and other matter. Along with rock mechanics, soil mechanics provides the theoretical basis for analysis in geotechnical engineering, a subdiscipline of civil engineering, and engineering geology, a subdiscipline of geology. Soil mechanics is used to analyze the deformations of and flow of fluids within natural and man-made structures that are supported on or made of soil, or structures that are buried in soils. Example applications are building and bridge foundations, retaining walls, dams, and buried pipeline systems. Principles of soil mechanics are also used in related disciplines such as engineering geology, geophysical engineering, coastal engineering, agricultural engineering, hydrology and soil physics.

Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the pressure relative to the ambient pressure.

Groundwater water located beneath the ground surface

Groundwater is the water present beneath Earth's surface in soil pore spaces and in the fractures of rock formations. A unit of rock or an unconsolidated deposit is called an aquifer when it can yield a usable quantity of water. The depth at which soil pore spaces or fractures and voids in rock become completely saturated with water is called the water table. Groundwater is recharged from and eventually flows to the surface naturally; natural discharge often occurs at springs and seeps, and can form oases or wetlands. Groundwater is also often withdrawn for agricultural, municipal, and industrial use by constructing and operating extraction wells. The study of the distribution and movement of groundwater is hydrogeology, also called groundwater hydrology.

In the narrow sense, "consolidation" refers strictly to this delayed volumetric response to pressure change due to gradual movement of water. Some publications also use "consolidation" in the broad sense, to refer to any process by which soil changes volume due to a change in applied pressure. This broader definition encompasses the overall concept of soil compaction, subsidence, and heave. Some types of soil, mainly those rich in organic matter, show significant creep, whereby the soil changes volume slowly at constant effective stress over a longer time-scale than consolidation due to the diffusion of water. To distinguish between the two mechanisms, "primary consolidation" refers to consolidation due to dissipation of excess water pressure, while "secondary consolidation" refers to the creep process.

Soil compaction process in geotechnical engineering

In geotechnical engineering, soil compaction is the process in which a stress applied to a soil causes densification as air is displaced from the pores between the soil grains. When stress is applied that causes densification due to water being displaced from between the soil grains, then consolidation, not compaction, has occurred. Normally, compaction is the result of heavy machinery compressing the soil, but it can also occur due to the passage of (e.g.) animal feet.

Subsidence is the sudden sinking or gradual downward settling of the ground's surface with little or no horizontal motion. The definition of subsidence is not restricted by the rate, magnitude, or area involved in the downward movement. It may be caused by natural processes or by human activities. The former include various karst phenomena, thawing of permafrost, consolidation, oxidation of organic soils, slow crustal warping, normal faulting, caldera subsidence, or withdrawal of fluid lava from beneath a solid crust. The human activities include sub-surface mining or extraction of underground fluids, e. g. petroleum, natural gas, or groundwater. Ground subsidence is of global concern to geologists, geotechnical engineers, surveyors, engineers, urban planners, landowners, and the public in general.

Organic matter, organic material, or natural organic matter (NOM) refers to the large pool of carbon-based compounds found within natural and engineered, terrestrial and aquatic environments. It is matter composed of organic compounds that have come from the remains of organisms such as plants and animals and their waste products in the environment. Organic molecules can also be made by chemical reactions that don't involve life. Basic structures are created from cellulose, tannin, cutin, and lignin, along with other various proteins, lipids, and carbohydrates. Organic matter is very important in the movement of nutrients in the environment and plays a role in water retention on the surface of the planet.

The effects of consolidation are most conspicuous where a building sits over a layer of soil with low stiffness and low permeability, such as marine clay, leading to large settlement over many years. Types of construction project where consolidation often poses technical risk include land reclamation, the construction of embankments, and tunnel and basement excavation in clay.

A building, or edifice, is a structure with a roof and walls standing more or less permanently in one place, such as a house or factory. Buildings come in a variety of sizes, shapes, and functions, and have been adapted throughout history for a wide number of factors, from building materials available, to weather conditions, land prices, ground conditions, specific uses, and aesthetic reasons. To better understand the term building compare the list of nonbuilding structures.

Stiffness is the extent to which an object resists deformation in response to an applied force.

Marine clay is a type of clay found in coastal regions around the world. In the northern, deglaciated regions, it can sometimes be quick clay, which is notorious for being involved in landslides.

Geotechnical engineers use oedometers to quantify the effects of consolidation. In an oedometer test, a series of known pressures are applied to a thin disc of soil sample, and the change of sample thickness with time is recorded. This allows the consolidation characteristics of the soil to be quantified in terms of the coefficient of consolidation ( $C_{v}$ ) and hydraulic conductivity ( $K$ ).

History and terminology

According to the "father of soil mechanics", Karl von Terzaghi, consolidation is "any process which involves a decrease in water content of saturated soil without replacement of water by air". More generally, consolidation refers to the process by which soils change volume in response to a change in pressure, encompassing both compaction and swelling.^[1]

Karl von Terzaghi was an Austrian Mechanical Engineer, geotechnical engineer and geologist known as the "father of soil mechanics".

Mechanism

Consolidation is the process in which reduction in volume takes place by expulsion of water under long-term static loads.

When stress is applied to a soil that causes the soil particles to pack together more tightly. When this occurs in a soil that is saturated with water, water will be squeezed out of the soil. The magnitude of consolidation can be predicted by many different methods. In the Classical Method, developed by Terzaghi, soils are tested with an oedometer test to determine their compression index. This can be used to predict the amount of consolidation.

Oedometer test ground-mechanical test device in which the load of soils can be studied

An oedometer test is a kind of geotechnical investigation performed in geotechnical engineering that measures a soil's consolidation properties. Oedometer tests are performed by applying different loads to a soil sample and measuring the deformation response. The results from these tests are used to predict how a soil in the field will deform in response to a change in effective stress.

When stress is removed from a consolidated soil, the soil will rebound, regaining some of the volume it had lost in the consolidation process. If the stress is reapplied, the soil will consolidate again along a recompression curve, defined by the recompression index. The soil which had its load removed is considered to be "overconsolidated". This is the case for soils that have previously had glaciers on them. The highest stress that it has been subjected to is termed the "preconsolidation stress". The "over-consolidation ratio" (OCR) is defined as the highest stress experienced divided by the current stress. A soil that is currently experiencing its highest stress is said to be "normally consolidated" and has an OCR of one. A soil could be considered "underconsolidated" immediately after a new load is applied but before the excess pore water pressure has dissipated.

Consolidation analysis

Spring analogy

The process of consolidation is often explained with an idealized system composed of a spring, a container with a hole in its cover, and water. In this system, the spring represents the compressibility or the structure of the soil itself, and the water which fills the container represents the pore water in the soil.

The container is completely filled with water, and the hole is closed. (Fully saturated soil)
A load is applied onto the cover, while the hole is still unopened. At this stage, only the water resists the applied load. (Development of excess pore water pressure)
As soon as the hole is opened, water starts to drain out through the hole and the spring shortens. (Drainage of excess pore water pressure)
After some time, the drainage of water no longer occurs. Now, the spring alone resists the applied load. (Full dissipation of excess pore water pressure. End of consolidation)

Primary consolidation

This method assumes consolidation occurs in only one-dimension. Laboratory data is used to construct a plot of strain or void ratio versus effective stress where the effective stress axis is on a logarithmic scale. The plot's slope is the compression index or recompression index. The equation for consolidation settlement of a normally consolidated soil can then be determined to be:

$\delta _{c}={\frac {C_{c}}{1+e_{0}}}H\log \left({\frac {\sigma _{zf}'}{\sigma _{z0}'}}\right)\$

where

δ_c is the settlement due to consolidation.

C_c is the compression index.

e₀ is the initial void ratio.

H is the height of the compressible soil.

σ_zf is the final vertical stress.

σ_z0 is the initial vertical stress.

C_c can be replaced by C_r (the recompression index) for use in overconsolidated soils where the final effective stress is less than the preconsolidation stress. When the final effective stress is greater than the preconsolidation stress, the two equations must be used in combination to model both the recompression portion and the virgin compression portion of the consolidation processes, as follows,

$\delta _{c}={\frac {C_{r}}{1+e_{0}}}H\log \left({\frac {\sigma _{zc}'}{\sigma _{z0}'}}\right)+{\frac {C_{c}}{1+e_{0}}}H\log \left({\frac {\sigma _{zf}'}{\sigma _{zc}'}}\right)\$

where σ_zc is the preconsolidation stress of the soil.

Secondary consolidation

Secondary compression is the compression of soil that takes place after primary consolidation. Even after the reduction of hydrostatic pressure some compression of soil takes place at slow rate. This is known as secondary compression. Secondary compression is caused by creep, viscous behavior of the clay-water system, compression of organic matter, and other processes. In sand, settlement caused by secondary compression is negligible, but in peat, a soil with very high organic content, it is very significant. Due to transfer of stresses to points of contact of soil grains some of the highly viscous water between the points of contact is forced out.

Secondary compression is given by the formula

$S_{s}={\frac {H_{0}}{1+e_{0}}}C_{a}\log \left({\frac {t}{t_{95}}}\right)\$

Where H₀ is the height of the consolidating medium
e₀ is the initial void ratio
C_a is the secondary compression index
t is the length of time after consolidation considered
t₉₅ is the length of time for achieving 95% consolidation

Time dependency

The time for consolidation to occur can be predicted. Sometimes consolidation can take years. This is especially true in saturated clays because their hydraulic conductivity is extremely low, and this causes the water to take an exceptionally long time to drain out of the soil. While drainage is occurring, the pore water pressure is greater than normal because it is carrying part of the applied stress (as opposed to the soil particles).

$T_{v}={\frac {c_{v}*t}{(H_{dr})^{2}}}\$

Where T_v is the time factor.

H_dr is the average longest drain path during consolidation.

t is the time at measurement

C_v is defined as the coefficient of consolidation found using the log method with

$C_{v}={\frac {T_{50}H_{dr}^{2}}{t_{50}}}$

or the root method with

$C_{v}={\frac {T_{95}H_{dr}^{2}}{t_{95}}}$

t₅₀ time to 50% deformation (consolidation) and t₉₅ is 95%

Where T₉₅=1.129 T₅₀=0.197

Related Research Articles

In probability theory, a log-normal distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable $X$ is log-normally distributed, then $Y = ln(X)$ has a normal distribution. Likewise, if $Y$ has a normal distribution, then the exponential function of $Y$ , $X = exp(Y)$ , has a log-normal distribution. A random variable which is log-normally distributed takes only positive real values. The distribution is occasionally referred to as the Galton distribution or Galton's distribution, after Francis Galton. The log-normal distribution also has been associated with other names, such as McAlister, Gibrat and Cobb–Douglas.

In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material. For example, when a solid vertical bar is supporting an overhead weight, each particle in the bar pushes on the particles immediately below it. When a liquid is in a closed container under pressure, each particle gets pushed against by all the surrounding particles. The container walls and the pressure-inducing surface push against them in (Newtonian) reaction. These macroscopic forces are actually the net result of a very large number of intermolecular forces and collisions between the particles in those molecules. Stress is frequently represented by a lowercase Greek letter sigma (σ).

Poisson's ratio, denoted by the Greek letter 'nu', $, and named after Siméon Poisson, is the negative of the ratio of (signed) transverse strain to (signed) axial strain. For small values of these changes, is the amount of transversal expansion divided by the amount of axial compression.$

Work hardening, also known as strain hardening, is the strengthening of a metal or polymer by plastic deformation. Work hardening may be desirable, undesirable, or inconsequential, depending on the context.

In the field of hydrogeology, storage properties are physical properties that characterize the capacity of an aquifer to release groundwater. These properties are Storativity (S), specific storage (S_s) and specific yield (S_y).

In geotechnical engineering, bearing capacity is the capacity of soil to support the loads applied to the ground. The bearing capacity of soil is the maximum average contact pressure between the foundation and the soil which should not produce shear failure in the soil. Ultimate bearing capacity is the theoretical maximum pressure which can be supported without failure; allowable bearing capacity is the ultimate bearing capacity divided by a factor of safety. Sometimes, on soft soil sites, large settlements may occur under loaded foundations without actual shear failure occurring; in such cases, the allowable bearing capacity is based on the maximum allowable settlement.

A triaxial shear test is a common method to measure the mechanical properties of many deformable solids, especially soil and rock, and other granular materials or powders. There are several variations on the test.

A yield surface is a five-dimensional surface in the six-dimensional space of stresses. The yield surface is usually convex and the state of stress of inside the yield surface is elastic. When the stress state lies on the surface the material is said to have reached its yield point and the material is said to have become plastic. Further deformation of the material causes the stress state to remain on the yield surface, even though the shape and size of the surface may change as the plastic deformation evolves. This is because stress states that lie outside the yield surface are non-permissible in rate-independent plasticity, though not in some models of viscoplasticity.

Lateral earth pressure is the pressure that soil exerts in the horizontal direction. The lateral earth pressure is important because it affects the consolidation behavior and strength of the soil and because it is considered in the design of geotechnical engineering structures such as retaining walls, basements, tunnels, deep foundations and braced excavations.

Terzaghi's Principle states that when a rock is subjected to a stress, it is opposed by the fluid pressure of pores in the rock.

Critical State Soil Mechanics is the area of soil mechanics that encompasses the conceptual models that represent the mechanical behavior of saturated remolded soils based on the Critical State concept.

In mechanics and geodynamics, a critical taper is the equilibrium angle made by the far end of a wedge-shaped agglomeration of material that is being pushed by the near end. The angle of the critical taper is a function of the material properties within the wedge, pore fluid pressure, and strength of the fault along the base of the wedge.

Preconsolidation pressure is the maximum effective vertical overburden stress that a particular soil sample has sustained in the past. This quantity is important in geotechnical engineering, particularly for finding the expected settlement of foundations and embankments. Alternative names for the preconsolidation pressure are preconsolidation stress, pre-compression stress, pre-compaction stress, and preload stress. A soil is called overconsolidated if the current effective stress acting on the soil is less than the historical maximum.

In solid mechanics, a reinforced solid is a brittle material that is reinforced by ductile bars or fibres. A common application is reinforced concrete. When the concrete cracks the tensile force in a crack is not carried any more by the concrete but by the steel reinforcing bars only. The reinforced concrete will continue to carry the load provided that sufficient reinforcement is present. A typical design problem is to find the smallest amount of reinforcement that can carry the stresses on a small cube. This can be formulated as an optimization problem.

According to the classical theories of elastic or plastic structures made from a material with non-random strength (f_t), the nominal strength (σ_N) of a structure is independent of the structure size (D) when geometrically similar structures are considered. Any deviation from this property is called the size effect. For example, conventional strength of materials predicts that a large beam and a tiny beam will fail at the same stress if they are made of the same material. In the real world, because of size effects, a larger beam will fail at a lower stress than a smaller beam.

Geotechnical centrifuge modeling is a technique for testing physical scale models of Geotechnical Engineering systems such as natural and man-made slopes and earth retaining structures and building or bridge foundations.

Lode coordinates $or Haigh-Westergaard coordinates . are a set of tensor invariants that span the space of real, symmetric, second-order, 3-dimensional tensors and are isomorphic with respect to principal stress space. This right-handed orthogonal coordinate system is named in honor of the German scientist Dr. Walter Lode because of his seminal paper written in 1926 describing the effect of the middle principal stress on metal plasticity. Other examples of sets of tensor invariants are the set of principal stresses or the set of mechanics invariants . The Lode coordinate system can be described as a cylindrical coordinate system within principal stress space with a coincident origin and the z-axis parallel to the vector .$

The microplane model, conceived in 1984, is a material constitutive model for progressive softening damage. Its advantage over the classical tensorial constitutive models is that it can capture the oriented nature of damage such as tensile cracking, slip, friction, and compression splitting, as well as the orientation of fiber reinforcement. Another advantage is that the anisotropy of materials such as gas shale or fiber composites can be effectively represented. To prevent unstable strain localization, this model must be used in combination with some nonlocal continuum formulation. Prior to 2000, these advantages were outweighed by greater computational demands of the material subroutine, but thanks to huge increase of computer power, the microplane model is now routinely used in computer programs, even with tens of millions of finite elements.

References

↑ Schofield, Andrew Noel; Wroth, Peter (1968). Critical State Soil Mechanics. McGraw-Hill.

Bibliography

Coduto, Donald (2001), Foundation Design, Prentice-Hall, ISBN 0-13-589706-8
Kim, Myung-mo (2000), Soil Mechanics (in Korean) (4 ed.), Seoul: Munundang, ISBN 89-7393-053-2
Terzaghi, Karl (1943), Theoretical soil mechanics, John Wiley&Sons, Inc., p. 265

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[1] Schofield, Andrew Noel; Wroth, Peter (1968). Critical State Soil Mechanics. McGraw-Hill.