Slopes and Related Topics

Slopes and Related Topics

ENV-2E1Y Fluvial Geomorphology

2004 - 2005

Slopes and related topics

Section 3 Consolidation behaviour of Sediments


N.K. ToveyENV-2E1Y: Fluvial Geomorphology 2004 - 2005Section 3

3. Consolidation behaviour of Sediments


N.K. ToveyENV-2E1Y: Fluvial Geomorphology 2004 - 2005Section 3

3.1 Introduction

This section of the course deals with how soils behave under load.

The term CONSOLIDATION is used to represent the process which occurs under a steady load, whether naturally applied or applied by man. There may be a loading arising from glaciation or sediment deposition. Equally, there may be sediment removal which will cause an unloading. Finally consolidation may also occur through natural or artificial ground water lowering.

The term COMPACTION is used to define a dynamic process of loading either by man or by earthquakes. Some textbooks use the term compaction to cover both consolidation and compaction.

There are two separate aspects to the consolidation process that we need to consider:-

1)the amount a soil compresses under a given load

2)the rate at which the soil compresses

We are interested in consolidation for several reasons:-

1)consolidation affects the properties of soils and in particular the shear strength.

2)we often wish to known how much consolidation will take place under a given load (and how fast, particularly if we are involved in draining areas of land.

3)we may wish to use consolidation in environmental reconstruction of the past form of the sediment (e.g. thickness of ice during glaciation etc.).

4)we may wish to correct for self weight consolidation in Quaternary studies to correctly reconstruct previous climates and sedimentation rates. Recent research by Tovey and Paul (2001) suggests that errors of over 50% may arise if such correction are not made.

3.2 Model Simulation (see Fig. 3.1)

The process of consolidation may be illustrated by a model which consists of a "weightless" piston inside a cylinder sitting on a spring. There is a pressure tapping in the cylinder so that changes in the water pressure may be monitored. At the base is a small hole connected via a stop cock to a fine bore tube which passes outside the cylinder to rest with its outlet below the water level in the reservoir above the piston. Initially the stop cock is closed and the system is in equilibrium with the water level in the manometer at the same level as that in the reservoir.

A weight (P) is now lowered onto the top of the piston. No load can be taken by the piston because the spring cannot compress, and so all the additional load is taken by an increase in the water pressure. If the weight is P Newtons, then the detected rise in water level in the manometer will be (Fig. 3.1b):-

...... 3.1

where A is the cross sectional area of the cylinder

The tap is now opened and immediately the water level in the manometer will begin to fall as water flows from within the cylinder to the reservoir above the piston (Fig. 3.1c). Eventually after a given time the water level in the manometer tube will have fallen back to its original level and at that time there is no excess pore water pressure and the extra load had been taken entirely by the spring (Fig. 3.1d). The time taken to reach this equilibrium will depend on the rate of flow possible through the fine bore tube.

The process of consolidation within a soil is almost identical to that described above. Initially, the whole of any extra load is taken by an immediate rise in the pore water pressure, and none of the extra load is taken by the soil fabric. After consolidation starts, progressively more and more of the additional load is taken by the soil fabric while the excess water pressure slowly falls and at infinite time will be zero once again.

The most important factor governing the rate of consolidation is the rate at which the water flows out. This of course depends entirely on the permeability of the soil. It is thus not surprising to note that Darcy's Law - i.e. the law relating the velocity of flow to hydraulic gradient will be a key consideration in the process of consolidation.

What happens if we now close the stop cock and remove the load from the piston.? Fig. 3.1d represents the situation if we closed the tap after the consolidation

As we remove the load, the spring initially cannot expand and so the water is placed under suction and the level of water in the manometer will fall by an equal and opposite amount to that specified by equation 3.1 (see Fig. 3.1e). The tap is now opened and the level in the manometer rises as water is sucked in from the reservoir and the spring relaxes. (Fig. 3.1f) Ultimately the piston and water level will return to their respective starting positions (Fig. 3.1g).

While the process of consolidation of a soil could be described fairly well by the model, the process of unloading a soil is very different from that in the model. Fig. 3.2 which shows a plot of voids ratio against stress illustrates this point.


N.K. ToveyENV-2E1Y: Fluvial Geomorphology 2004 - 2005Section 3

Fig. 3.1. Model Simulation of the Consolidation Process


N.K. ToveyENV-2E1Y: Fluvial Geomorphology 2004 - 2005Section 3

Fig. 3.2 Schematic representation of consolidation of soils. During consolidation, soil follows upper line. During rebound, the lower line is followed. Most soils exhibit both elasticity and plasticity.

During loading the soil follows an exponential decay curve. If it were to follow the process described by the model during unloading, then the process would be elastic and the unloading curve would be identical with the loading curve. In fact the unloading curve usually follows a second exponential curve, but this time it is much lower than the original loading curve. In extreme circumstances, the unloading curve may be horizontal (i.e. there is no rebound whatsoever).

A material which follows the same curve on loading and unloading is known as an elastic material. A special case of an elastic material is one which shows a straight line loading and unloading relationship (e.g. steel below its yield stress).

A material which has no recovery at all (i.e. the unloading line is horizontal is a perfectly plastic material.

Most soils exhibit some rebound and therefore may be called elasto-plastic. On the graph in Fig. 3.2, the area between the horizontal line and the actual rebound line indicates the elastic recovery, while that between the loading and unloading lines is the permanent plastic deformation of the soil

In soil fabric terms, elasticity arises because during loading some particles are bent and stored strain energy which is released on unloading. The plastic component arises from the collapse of the initial soil skeleton with the rearrangement of the particles into a more parallel alignment.

3.3 General Statements about Consolidation

In this course we need to consider the processes which are occurring and to use some of the key results to solve problems. As with the section on Seepage, there are some sections which relate purely to the mathematically derivation of the key formulae, and these sections are "boxed", and may be omitted by those who are not mathematically inclined. In most cases, there are graphical solutions, or methods which require the application of simple formulae.

3.3.1 The Assumptions made

The are several assumptions made in the theory of consolidation, but the key ones are: -

1)Water is incompressible (i.e. it does not change in volume on compression).

2)The soil particles are incompressible.

3)Only one-dimensional consolidation is present, i.e. flows of water, settlement and the applied load all act in one direction which is usually vertical. This assumption is not necessary, but it makes the deviation easier if we assume a purely 1-D situation.

4)Darcy's Law is valid

5)The initial excess load is initially taken solely by a rise in pore pressure

A consequence of assumptions 1 & 2 is that the net flow of water from an element of soil equals its reduction in volume.

When we considered ground water flow in the previous section, it was assumed there was no reduction in volume, and no accumulation or net removal of water. In this section we allow for volumes of soil to change. In Hydrogeology, the term Compressible Aquifer is used and this is exactly the same as a soil collapsing under consolidation.

Fig. 3.3 illustrates the consolidation process. The element of soil has water flowing through it (upwards in this case), but the flow of water is greater at the top because of the water squeezed out from the volume itself.

3.3.2 Key factors affecting consolidation

While we do not expect you to reproduce the derivation of the consolidation equations, it is important you understand the fundamental principles behind them.

Fig. 3.3 Illustration of the consolidation process. Water is squeezed out from the element and the flow of water outwards is greater than that flowing in.

First let us consider what form we would like the equation to be in. Essentially, form the introduction we require an equation which relates effective stress (or pore water pressure) to both, time and the changing thickness of the soil. To determine the governing equations, we consider an element of soil of thickness z and area A. There are four points to consider.


The layer is compressing and as it does so water is squeezed out, and the velocity of the water at the top (assumed to be nearer the drainage surface) will be greater than the flowing in. Also the volume of water squeezed out will equal the change in volume of the element of soil. We use this latter fact in one of the governing equations, i.e. the CONTINUITY EQUATION which in this situation may be specified as:-

The change in volume of the soil element = net outflow of water.


DARCY'S LAW describing the flow of water in a soil may be used to specify how the velocity of the water is changing.

DARCY'S LAW may be specified as:-

Velocity of water = coefficient of permeability x hydraulic gradient .


In attempting to work out the change in volume of the soil element, it is only the voids that change in size, the solid volume remains constant.


During consolidation the extra load is assumed to be taken initially by an excess pore water pressure and that this pore pressure dissipates as the effective stress increases as the soil fabric adjusts to the new load:-

thus the change in pore pressure = change in effective stress,

i.e. u = 1

The last two factors, together with the statement of continuity and Darcy's Law, are sufficient to define a consolidation equation relating how the pore pressure varies, both with time and depth.

In the analysis on the next three pages two terms are used for convenience:-:

i)mvc - this equals the gradient of the line at the point in question on the voids ratio versus stress graph multiplied by the factor:-


mvc is known as the coefficient of compressibility and is of considerable importance in predictions of settlement.

Note: in some text books, mvc is given the symbol mv.

The factor 1 / (1 + eo) arises because the graph is given as voids ratio, and we need to convert to total volume of soil.

ii)Cvc equals

This is a substitution made merely for convenience. Cvcis known as the coefficient of consolidation as is of importance if we wish to know the rate at which consolidation is proceeding. It should be noted that this term includes k, the coefficient of permeability.

Note: in some textbooks, cvc is given the symbol cv.

If we go through the full derivation we will eventually obtain the desired equation, i.e.

...... 3.2

This relates the rate of change of pore pressure with both time and depth. This is a standard form of an equation known as the diffusion equation for which standard solutions are available in text books. This equation has been solved and we do not need to resolve it as we can use the graphical solutions to all our problems. If you are doing the ENV-2A21?ENV-2A22 Mathematics Units you may wish to attempt to solve the above as an environmental application of maths.


You should, however, be clear of the steps outlined above, as what follows is nothing more than the mathematical representation of the above.

3.5 Consolidation behaviour of Soils

3.5.1 Amount of Consolidation with Load

Fig. 3.4 Typical Voids ratio - effective stress curve for a soil

The consolidation behaviour of soils studies both how much a soil consolidates under a given load and also how fast it consolidates. The behaviour with load is normally displayed as a graph as shown in either Fig. 3.4 or Fig. 3.5.

After sedimentation a soil will normally be under an effective stress consistent with the weight of sediment above. It will initially have an open structure so that the voids ratio is high as indicated by point A in Figs 3.4 and 3.5. The exact voids ratio depends on the actual clay present but may be as high as 10 or more.

As more sediment is laid down on top, the soil compresses and follows the curve AB. At B the soil is unloaded (perhaps following ice retreat after glaciation, or the erosion of sediments above and follows the unloading curve BCD. In extreme cases, and particularly if the soil is largely sand, the unloading curve may be horizontal.

If the soil is loaded again it tends to follow a line slightly above the original unloading curve as shown by DEB (i.e. there is a hysteresis loop BCDEB), until the loading reaches the previous maximum stress level as denoted by B. After this the loading curve follows a continuation of the original curve AB along BF.

The loading and unloading sequences may be studies more readily if the X-axis (abscissa) is plotted as the logarithm of the effective stress as shown in Fig. 3.5.

Fig. 3.5 Voids ratio against logarithm of effective stress

Fig. 3.5 shows that all the consolidation and unloading lines become straight lines, and both the unloading and reloading lines approximate to the same line and it is convention to treat these as being the same.

These consolidation curves are very powerful tools not only in understanding how a soil will behave in the future, but also to attempt environmental reconstruction as to what has happened in the past. The line ABF is known as the VIRGIN (or NORMAL) CONSOLIDATION LINE.

A soil can only exist in EQUILIBRIUM in the region below and to the left of the line ABF. The soil may temporarily exist above and to the right of the line, but it is not then in equilibrium and will be unstable (in the case of quick clays see below), or in transition through dissipation of pore water pressure (also see below).

We can replicate the above process in the laboratory doing a consolidation test similar to the one you have or will be doing in a practical session. We use the consolidometer to measure the consolidation characteristics by adding a series of loads, allowing the soil to reach equilibrium and then measure the settlement before adding the next load. The point at which equilibrium is achieved is measured separately and is covered in a later section.

3.5.2 Simple Environmental Reconstruction using a consolidation test

Fig. 3.6 shows a typical plot from a soil which has been sampled. From the borehole log and the unit weight information we can estimate the current in situ stress level on the sample (see the worked example given as a handout at the end of the introductory section). [ Remember to allow for the buoyant effect of water!!]

Fig. 3.6 Example of Environmental Reconstruction

When we extract the sample from the borehole, the in situ stress is released as we extract the core. At this point we do not know the unloading curve. We place the same in a consolidometer and load the sample in the normal way. It will follow an approximately straight line DB (in Fig. 3.6). The point X represents the previous in situ load, and not infrequently the sample will continue on beyond this to the point B, where the line will kink and follow the line BF. BF clearly represents the VIRGIN CONSOLIDATION LINE, while DXB is the reloading line.

Sometimes both B and X coincide, in which case the sample is normally consolidated and has NEVER in the past been loaded beyond its present level of loading. More usually, B is to the right of X which indicates that the soil isOVERCONSOLIDATED

We may read off the previous maximum consolidation stress from the graph. If we subtract the present in situ stress level, the difference will represent the previous additional load which was on the soil. If we know that this came from glaciation (from a study of the geology of the area), the since the unit weight of ice is 9 kN m-3, we can readily estimate the thickness of ice that covered the area. Equally, the additional loading may have arisen from additional sediment which has subsequently been eroded. Whatever the cause, this gives us a method to establish what the magnitude on the loading was.