3.1 INTRODUCTION
All earth buildings have the same ingredients: a graded mixture of subsoil, water and, in some cases – stabilisers such as Portland cement, lime, bitumen or straw. Wall construction takes place using a mixture with an optimum water content to allow good compaction, from which evaporation occurs and the wall gains strength: it is therefore clear that the water in the mix has an important role. But the mechanisms by which strength
develops and changes over time in these materials have rarely been rigorously examined, and effective conservation would seem to be handicapped
without this understanding.
This chapter covers the physical basis for the development of strength in earthen construction materials, and begins with some basic soil
mechanics, followed by an examination of the behaviour of earthen construction materials at the particle level. The fundamental and most
important source of strength in unstabilised earthen construction materials is shown to be due to the small amounts of water held in the earth mixture at particle contacts, and in clay bridges between larger particles. The striking example is that of a sandcastle, where too much water makes the castle flow away and too little makes it blow away.
Improved understanding of the role of water in earthen construction materials at the particle level is used in later chapters to inform conservation strategies for heritage structures.
3.2 SOIL MECHANICS
Civil engineers refer to the subsoil (below the topsoil, the zone in which plants grow) or earth used for building as soil, and to the study of its behaviour as soil mechanics. This encompasses methods of determining the strengths and stiffness of soils: strength for
determining the stability and safety of structures built in or on soil, and stiffness for determining movements during use (of tunnels, foundations, retaining walls etc.). Topsoil is not used for earth building, and will not be considered further here.
Soil is an accumulation of mineral particles formed by the weathering of rocks. The type of soil depends on the rock from which it originates, and on the processes it has undergone since weathering. A soil is often described by the distribution of particle sizes it contains, and names given to ranges of particle sizes are shown in Table 3.1. (Different conventions are used in different parts of the world; the table shows the classifications used in the UK.) Particles smaller than 0.002 mm are termedclay , and are often considered to be different from larger particles because of the relative importance of the electrostatic charges held on the surfaces of clay particles. In fact, this feature of clays has little effect on their strength.
Table 3.1: Particle sizes to BS 1377[51]
Name Maximum dimension (mm)
Clay 0.002
Silt 0.06
Sand 2
Gravel 60
Cobbles 200
Boulders > 200
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In its natural state soil consists of interlocked solid particles with voids (or pores) between. These voids are filled with fluid: this is usually air or water, but other fluids (such as oil) can be present. Where all the pores in the soil are filled with water, the soil is described as saturated; where air is present in some of the pores, the soil is described as unsaturated. Most earthen construction materials (which can be regarded as manufactured soils) are unsaturated.
However for most conventional construction projects civil engineers usually assume soils to be saturated, and the established theories of soil strength have been based on this assumption. This is the natural starting point for an explanation of soil mechanics.
3.3 SOIL STRENGTH
Soil strength usually refers to soil shearstrength, as soils have little or no tensile strength; they usually fail in shear. We refer in this chapter mainly to uncemented soils, but for cemented soils (stabilised rammed earth, cement-stabilised block, or rocks such as sandstone) tensile failure is possible. It is now widely accepted that the source of a soil’s strength (clays included) lies in the friction between particles[52]. Friction is a concept familiar from school physics, usually demonstrated by a simple block on a plane, as shown in Figure 3.1.
φ R N
F
Figure 3.1: Simple model of friction, showing friction angleφ
When the block is just about to slide, a force Fis resisted by friction between the block and the plane beneath. The magnitude of the resisting force is determined by the value of the normal forceNand the coefficient of friction μbetween the block and the plane. The resultant forceRis oriented at an angleφ to the vertical, where μ= tanφ . The angleφ provides a
measure of the shear strength of the assembly through the following equation:
F= μR = R tanφ (3.1)
For soils we measure shear strength via a
macroscopic angle of frictionφ (rather than looking at individual contacts), which is associated with the angle of repose (slope) of a pile of soil. For sands and gravelsφ can rise to 40°, but for most soils it lies between 15° and 30°. Engineers determining the possibility of soil failure use the following equation for points in the soil mass:
τ =σ ′ tan φ ′ +c (3.2)
whereτ is the shear strength, i.e. the shear stress on a plane just at the point of failure, and φ ’ is the effective angle of friction. The dashed superscripts indicate that these are ‘effective’ values (see below).
This deals with the frictional strength of soils. If there is cementation between the soil particles (for instance in stabilised rammed earth) then in addition to the frictional strength there will be a component of apparent cohesive strength (c) which does not vary with the applied normal stresses unless the cementitious bonds are broken.
3.4 EFFECTIVE STRESS
Saturated soils contain water in the interparticle voids (the pore water), and one of their most important features is that failure can occur both from changes in the applied load and from changes in the pressure in the pore water. The theory of effective stress states that the behaviour of soils is governed by a single stress (the effective stress), which is defined as:
σ′ = σ – u (3.3)
whereσ is the total stress (the stress due to the applied loads) andu is the pore water pressure.
So ifσ rises oru falls, then the effective stress rises.
The effective stress is the normal stress that controls frictional behaviour, and so in either of these cases the shear strength increases. Alternatively, a rise in pore water pressure (i.e. a reduction in effective
FUNDAMENTAL BEHAVIOUR OF EARTHEN CONSTRUCTION MATERIALS 29
stress) can cause a failure with no change in applied loads. Examples of such behaviour are subsidence due to a rising water table, or landslides induced by rainfall. Therefore, unlike many other construction materials, the presence of water in soils makes their behaviour more complex.
3.5 UNSATURATED SOIL MECHANICS The soil mechanics routinely used by engineers assumes full saturation and effective stress
parameters, as described above. However, many conditions in the field are unsaturated. That is, the voids between soil particles are not entirely filled with water; air is present too. This seemingly innocuous change has a major influence on the mechanical and hydraulic behaviour of the soils.
Earthen construction materials are never completely dry, but nor are they saturated (if they were, one could not add more water to them). Materials such as rammed earth, cob and adobe are effectively manufactured unsaturated soils. In what follows we examine some of the theories that attempt to explain observed macroscopic unsaturated behaviour by looking at the particle level.
3.6 FUNDAMENTALS
A highly simplified model of an unsaturated soil comprises spherical particles linked by water held in
‘bridges’ between particles, as shown in Figure 3.2.
This allows us to make assumptions about the distances and interactions between particles, and allows us to undertake much simpler modelling.
We can then apply the properties of this simplified model to real soils.
The shape and size of the water bridges are determined by various physical properties and effects. The most fundamental one is thecontact angle. This is the angle that a water/air interface makes at a solid surface. If we imagine a drop of water on a smooth solid surface, we can clearly see the contact angleθ (Figure 3.3). For hydrophilic materials the contact angle is between zero and 90°. For hydrophobic materials the contact angle is between 90° and 180°.
Water Soil particles
Air
Figure 3.2: Simple model of an unsaturated soil
Water droplet
Figure 3.3: Contact angle of a droplet of water.
Courtesy of Richard Iles
The second fundamental property of the water held at bridges is surface tension, which exists at any water/air interface. Surface tension arises from the different forces on water molecules close to the interface compared with those in the body of the water. A molecule located within the body of the water is subject to equal attraction in all directions, whereas at the surface the absence of equal attraction in all directions leads to a net attractive force in the plane of the surface, known as the surface tension. For a large body of water the water surface will be flat, and only at the extreme edges will the surface curve to follow the contact angle. For a narrow pore containing water the two solid surfaces are close together, and the water surface will then be curved, forming the menisci seen in Figure 3.2.
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In this situation, and because of surface tension, equilibrium can occur only if there is a net pressure difference between the water and the air. The curvature of a meniscus is linked to this pressure difference by the Young–Laplace equation:
^
ua ± uwh
=T sc
r 1x +r 1ym
(3.4)Whereuais the air pressure, uwis the water pressure,
T sis the surface tension, andr xandr y are the radii of curvature of the meniscus. Considering the case of the idealised unsaturated soil, if the air pressure in the pores is atmospheric, Equation 3.4 implies that the water pressure is negative, so that both sides of the equation yield positive values, and this is indeed the case. This negative pressure is often referred to as a positive ‘suction’ (denoted by s, and defined as the difference between the air and water pressures,
ua–uw). Therefore the presence of air in the pores means that water is held between the particles in menisci with curvature. These cannot exist in equilibrium without there being a pressure difference across the air/water interface. With the air pressure at atmospheric, equilibrium can be reached only if there is a negative pressure in the water. This suction then provides an additional force pulling particles together (see Figure 3.4) and, crucially, an additional normal force between the soil particles that increases the macroscopic shear strength of a sample. The presence of suction then can be seen to strengthen an unsaturated soil as compared with its saturated state, and these ‘liquid bridges’ contribute to the strength of earthen materials.
Additional normal force between particles
Suction in water
Figure 3.4: The role of suction between two particles
3.7 RELATIVE HUMIDITY
All air contains water in vapour form, so the air held in pores will itself contain water vapour.
Relative humidity is a measure of the amount of water vapour in the air. A body of water contains water molecules in constant random motion;
the magnitude of this motion is determined by temperature. At the surface of the water body some molecules have sufficient momentum to escape from it, and join the water molecules present as vapour in the air surrounding the water. Molecules as water vapour are also in random thermal motion, sometimes losing energy and returning to liquid water. When the number of molecules leaving the water equals the number of molecules arriving, an equilibrium state is reached. When more
molecules are leaving than arriving, the liquid water is evaporating; when more molecules are arriving than leaving, the water vapour is condensing into liquid water. The different gases in air (e.g. water vapour, oxygen and carbon dioxide) exert different
partial pressures on their surroundings as a result of their different molecular kinetic energies. The partial pressure associated with the water vapour is referred to as the water vapour pressure. Relative humidity (RH) is a measurement of how much water vapour is present in the air as a proportion of the maximum amount there could be (which is determined by temperature, and is termed ‘saturated’1). It is
defined as the ratio of the water vapour pressure pv
to the vapour pressure when the air is saturated, p0: (3.5) There is a relationship between the suction in the menisci between particles and the relative humidity known as the Kelvin equation:
(3.6) Where R is the universal gas constant,Tis
temperature (in degrees K), and vw is the molar volume of water. By combining Equations (3.4) to (3.6) we can remove the suction term, to give:
(3.7)
1 Do not confuse this use of ‘saturated’ with the earlier use to refer to soil with water and no air in the interparticle pores.
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FUNDAMENTAL BEHAVIOUR OF EARTHEN CONSTRUCTION MATERIALS 31
Equation 3.6 is plotted in Figure 3.5. This shows that when the relative humidity is around 100%, suctions in equilibrium lie between 1 and 3000 kPa, but when the relative humidity reduces to 50% the suction increases to over 100 000 kPa.
It is also possible to link the radius of curvatures of the menisci to RH. For the case of a pore
idealised as a cylindrical tube, the radii of curvature are equal,r x =r y =r, and Equation 3.7 can be
% Plotting this equation (Figure 3.6) then shows
80 the equilibrium size of pore for a given relative
60 humidity. If RH is gradually lowered, pores will
empty (and fill with air) according to this plot. This
40 relative humidity (or more commonly suction) value
20 is known as theair entry value.
0
10 100 1000 10 000 100 000 1 000 000 Suction (kPa)
Figure 3.5: Plot of the Kelvin equation linking relative humidity to suction
If the relative humidity rises in an unsaturated soil, then water condenses from vapour in the pores to liquid water in the menisci. If we assume that the volume of the pores remains unchanged, then the radii of the menisci must increase. We can see from Equation 3.4 that this means the suction reduces.
Therefore climatic rises of humidity are likely to reduce the strength of earthen materials.
The attractive force provided across a liquid bridge is small, but if we use the simple idealisation of spherical particles (Figure 3.4), we can identify two components of this force: (a) the surface tension of the meniscus acting around the perimeter,F tension
and (b) the force arising because the pressure in the water is lower than the air pressure,F pressure. We can write these as follows:
F tension= 2π r neck T s (3.8)
F pressure= π r neck 2(ua – uw) (3.9) whererneck is the radius of the neck of the liquid bridge.
0.0001 0.001 0.01 0.1
Pore radius at air entry value (mm)
Figure 3.6: The relation between relative humidity and pore radius
3.8 THE SOIL WATER RETENTION CURVE For each unsaturated soil at a given state (i.e. a given compaction) there is a relationship between the water content and the suction, called the soil water retention curve (SWRC). The SWRC is a function of the void size distribution, and it also differs if the soil is wetting or drying – so-called hysteretic behaviour. A typical SWRC is shown in Figure 3.7, where, in
line with usual practice in geotechnics, thedegree of saturation (rather than the water content) is plotted
against suction. The degree of saturationSr is the ratio of the volume of water in a sample to the total volume of voids (i.e. Sr = 1 for a saturated soil, because all the pores are filled with water).
1 3
0 1
0 Air entry value Suction (s) (log scale) Residual air content
Figure 3.7: A typical soil water retention curve
The SWRC has some important features:
• The air entry value: this is the value of suction that must be exceeded for liquid water to begin to leave and air to enter.
• The residual saturation: this is the water content that can be achieved by normal drying processes.
This leaves water at the particle contact points and adsorbed to the surface of some particles.
To reach lower water contents requires artificial drying processes (such as heating above 100 °C), which are not usually found in nature.
• The residual air content: this is the volume of air that remains in a soil when it is wetted from dry. This is air that is trapped within pores, and is unable to escape.
As the water content of a soil increases, the value of suction reduces, following a wetting curve, and as the water content decreases, a different drying curve is followed. The significance of hysteresis here is that, for a given water content, the suction can be significantly different depending on the path travelled to reach that state. This has implications for earthen structures, because although we may be able to measure water content relatively easily, this does not tell us the suction unless we know the path (and without the suction we do not have a clear idea of the strength). Various reasons suggested for this hysteretic behaviour are suggested in the literature[53, 54].
The size and shape of the SWRC depend on the void size distribution of the soil, which as described earlier is a function of the particle size distribution and the compactive energy.
3.9 COMPACTION
Earthen construction materials are created with a degree of compaction (i.e. volume reduction), which creates a higher density material. Rammed earth and compressed earth blocks use mechanical force applied to the soil mixture to achieve this.
Compaction plays a major role in the formation of the pore size distribution, and therefore in the strength of the material.
Compaction is the process whereby the volume of a soil is reduced, causing air to be removed from the pore spaces, leading to an increase in the density and degree of saturation of the soil. The degree of compaction of a soil is measured by the dry density (the mass of solids per unit volume of soil) and depends on the initial water content and the amount of energy supplied – the compactive effort. For a given soil and compactive effort there is an optimum water content (OWC) at which maximum compaction, and thus dry density ( ρd) will occur (which is the desired state). If the soil is too dry, the particles are unable to rearrange into a denser formation.
If the soil is too wet, the pores are mostly filled with water, and the compactive effort will simply attempt to compress the water, but as this can be considered to be incompressible, an increase in density cannot be achieved.
There are several standard laboratory tests to determine the OWC for compaction of a sample, such as the standard or heavy Proctor tests, or the vibrating-hammer test. Each test uses a standard (but different) compactive effort, and each is appropriate for specific soils. Soils with larger particles are
compacted in larger moulds: thus the OWC for a gravel would be determined using a vibrating-hammer test, whereas a Standard Proctor test would be used for a clayey material. For modern rammed earth construction the Standard Proctor test is used to determine the OWC. Compaction test results are invariably plotted in the form shown in Figure 3.8.
The peak in the compaction curve indicates the OWC for that soil using that compactive procedure.
Compaction of earth-building materials is further complicated by the fact that often the compaction procedure occurs in layers (e.g. for rammed
Compaction of earth-building materials is further complicated by the fact that often the compaction procedure occurs in layers (e.g. for rammed