WALL DEFORMATIONS AND THEIR IMPLICATIONS

If the wall is relatively slender and vulnerable to overturning, the particular nature of the construction becomes important. One aspect of this is dis-cussed in Section 3.4, but there is a broader question of how easily the wall can bend or shear in response to the earth pressure acting on it. This is a consideration for any earth retaining structure, but the particular nature of drystone construction allows parts of the wall to separate from each other, reducing the resistance.

Deformation in bending is shown in Figure 3.3a. In most engineering materials, bending results in a compression on the side away from the pres-sure and an extension on the side facing the prespres-sure. So in the case of a retaining wall, the face would be shortened and the back lengthened.

However, this will happen only if a material compresses as easily as it stretches, and this is not the case for drystone construction. Because the stones are usually strong and stiff in relation to the loads they are carrying, very little compression can take place, so the face of the wall will not shorten significantly. On the other hand, the stones at the back of the wall are simply sitting on top of each other, and so can be lifted off each other. Significant bending deformation can therefore take place only if the overall vertical

stress within the back of the wall has reduced to zero. If the back of the wall is tending to lift up, then the full frictional resistance will be mobilised to resist that movement, so stones will tend not to lift, until the entire wall fails in overturning. The assessment of whether this can happen then becomes very similar to the assessment described in Section 2.4.2 and Figure 2.13.

The position of the resultant force may be considered at any level within the structure, in a similar way as was done for the base of the structure.

If the resultant force at a level within the wall lies in front of the middle third, this does not necessarily imply that the blocks at the back of the wall would lift up, merely that they will not be carrying a vertical load; the earth pressure on their backs would be pressing them against the blocks in front of them, and the friction on those blocks would be supporting the weight of the blocks at the back of the wall. This would introduce a shear stress on a vertical plane within the wall – this always occurs when anything bends.

For the structure to deform in pure bending requires a shear connection between the blocks at the front and the blocks at the back of the wall.

This may be provided by through-stones, or by having good overlaps as shown in Figure 3.2. Well-packed fill between front and back facing stones is unlikely to have the same effect – the wall will deform in shear.

Shear deformation is illustrated in Figure 3.3b. In one sense this is an easier type of deformation than bending for a wall made of rigid blocks. If the blocks make up layers, then shear deformation only requires one layer to slide on the layer below. On the other hand, drystone walls are usually made of rocks with rough surfaces and good frictional resistance, which makes this type of deformation difficult to achieve. Walls made of horizon-tally laid slate, with smooth surfaces with only moderate frictional resis-tance, could be liable to this type of deformation. Nevertheless, because this mode does not require blocks to actually lift up, a modest amount of shear deformation may take place as loads are applied to a wall, and in the full-scale experiments at Bath, a few millimetres of shear deformation occurred as the backfill was placed, arising from very small movements of

(a) (b) (c)

Figure 3.3 Wall deformations. (a) Bending deformation. (b) Shear deformation. (c) Com-bined bending and shear.

stone on stone as the friction between the stones quickly attained the value required to maintain equilibrium.

A combination of shear and bending, as shown in Figure 3.3c, is much more likely to occur in a drystone wall. This is because even though stones may not slide over each other easily, nor be lifted up easily, they may be able to rotate. The construction of the wall should make this difficult – a fully bonded construction will help, as will good use of through-stones and tightly packed, strong, angular fill.

Figure 3.4 shows how such an effect may arise in a fully bonded wall. It should be borne in mind that this is only a schematic representation, and that three-dimensional effects that cannot be shown here make the real behaviour more complex. However, this shows how the accumulated rota-tions and displacements of individual blocks can result in an overall shear-ing and bendshear-ing of the structure. Individual blocks tend to rotate because they are being pushed at the back and restrained at the base. Blocks that in this cross-sectional view are wide in relation to their height (i.e., have a high aspect ratio) will not rotate easily. The blocks that experience the greatest rotational forces are those at the toe of the structure, and if these blocks have a low aspect ratio (so they tend towards a square or round cross-section), then they could rotate and overturn, taking the rest of the wall with them. It is therefore not good practice to lay stones along the face of a wall, though because of the three-dimensional nature of the wall, infrequent stones laid in this way are unlikely to lead to a collapse.

The behaviour of a wall that has a front and back face and packed ‘fill’ in between depends on whether or not through-stones are used. The situation

(a) (b)

Figure 3.4 Rotation of stones within a fully bonded wall. (a) Before and (b) after.

without through-stones is shown in Figure 3.5. The front and back faces are to an extent free to behave independently, with bending deformations arising from rotation of the stones with lower aspect ratio, and the fill material compressing and being rearranged in response to this. The earth pressure exerts a bending moment on the entire structure, but for the struc-ture to respond as one, requires a shear stiffness within the fill which is just not there. So instead of behaving as a deep cantilever with high bending stiffness and strength, the front face and back face respond separately, pro-viding very much less resistance.

Through-stones restrain the front face and the back face from moving apart as the fill settles, so helping to maintain its tight packing, but they also restrict the rotation of the stones immediately above and below them. By ensuring that the weight of the wall and the fill is transferred into the front and back face, they also help to prevent sliding. The result is that the wall below each through stone is very much more rigid, but the through-stones also help the wall to behave as a single cantilever, with greatly increased bending stiffness.

The walls shown in Figures 3.4 through 3.6 are relatively wide, hav-ing proportions that an engineer might expect to produce a good factor of safety. The behaviour changes if the walls are more slender, which can work perfectly well and was normal for older walls. Figure 3.7 shows a wall with proportions that would lead to acceptable factors of safety with

(a) (b)

Figure 3.5 Rotation of stones within a wall – front and back face, with fill in between.

(a) Before. Note that this fill has not been packed well, for illustrative pur-poses – a waller who used no through-stones would probably not be very good! (b) After. Note that both the front and back faces are bent forward, while the fill at the base has been compressed laterally, and that higher up the wall has settled.

(a) (b)

Figure 3.6 Rotation of stones within a wall – front and back face, with through-stones.

(a) Before. Note that the through-stones would be at intervals along the length of the wall as well as up its height, so this two-dimensional repre-sentation has inevitable shortcomings, but it nevertheless can illustrate the constraints the through-stones impose on the deformation of the structure.

(b) After. There is hardly any change in response to the application of earth pressure. The through-stones not only tie the front and back faces together;

they also increase the pressure on the facing stones, making it much less likely that they will move.

Figure 3.7 A slender wall without through-stones. Having less fill between the front and back faces enables some direct interaction to occur between the larger stones, so this wall may be stiffer than the wider wall shown in Figure 3.5.

good quality backfill. Even without through-stones, the wall may be stiffer than the wider wall because the stones forming the front and back faces are now close enough together to interfere with each other, as shown in Figure 3.7, so the wall behaves more monolithically. The wall with through-stones will be stiffer still. Nearly all the main stones shown in these illustrations are relatively wide, with parallel top and bottom faces, and so they do not rotate easily. Figure 3.8 shows more realistically shaped stones, allowing the importance of unevenness in the stones to be seen more clearly.

The difference between these two-dimensional representations and the three-dimensional reality makes irregularity in the stones more important, as this introduces two more axes about which they can rotate. Rotation in plan, allowing one side of a stone to move forwards more than another, enables significantly more movement to take place as the stones move to a new position; this is likely to be accompanied by some movement about the third axis, in which the stone tilts along the length of the wall, whereas the cross-sections only show tilting across the width of the wall.

If smaller, narrower stones are used, with surfaces that are convex rather than flat, then they can rotate much more easily and larger deformations will result. The amount by which the wall deforms becomes particularly sensitive to the skill and care that has been exercised in placing the stones.

The use of pinnings (small blocks or wedges of stone) to stabilise the main stones can become almost inevitable if the builders are concerned to pro-duce an even face to the structure. Because of this sensitivity to the finest details of the construction of a highly variable material, deformations are

Figure 3.8 The effects of geometrical variations in the stones. This cross-section is less schematic than those in the previous illustrations, showing how the same stones can alter their positions to fit together in slightly different ways as the wall deforms in response to the load on its back. The more loose the original construction, the more it will deform.

likely to be uneven. Nevertheless, skilled builders can produce a wall that might deform by less than 1 in 1000 as it is loaded; this was shown in the first, highest quality test wall built at Bath which was monitored to mil-limetre accuracy.

3.6 BULGING

Drystone walls often display pronounced bulges in their faces, most typically centred at about a third of their height. Some are the first stages of a collapse, while others probably form soon after construction and remain unchanged.

Some observers will say simply that ‘bulging is a three-dimensional prob-lem’, but in fact long stretches of wall can show a continuous bulge, so this statement is simplistic. It is therefore essential to consider what gener-ates bulging that might be represented on a two-dimensional cross-section, before going on to consider three-dimensional bulges, which may exist over very short lengths of wall and could be a different kind of phenomenon.

3.6.1 Two-dimensional bulging

In considering bulging of any kind, it is important to take into account that the wall has changed from a presumably flat faced condition into a bulged condition, and then stopped moving. It therefore seems self-evident that the wall was not stable in its initial condition, and became stable in its bulged condition. The only plausible reason for questioning this would be if the bulging was a slow deformation that took place while a particularly severe load was applied, which then stopped when the load was removed. If this were the case, one would have to admire the ductility of the structure that could allow such deformation to take place while continuing to support the load, and wonder why the deformations did not accelerate; it is much more plausible that the deformed structure supports the load better, as a stretching spring ceases to stretch when it is in equilibrium with the load hung from it.

A stable two-dimensional bulge can develop because of the interaction between the backfill and the wall. The downwards component on the back of the wall due to friction can result in the back of the wall being com-pressed vertically more than the front of the wall over much of its height;

this can be seen by considering the position of the resultant force in Figure 3.1a. This causes the top of the wall to tilt back a little, which reduces the earth pressure acting on it; this tilting is enabled by the lower part of the wall tilting forwards under the action of the higher earth pressure at this greater depth. The improved stability of the deformed wall was demon-strated by Mundell et al. (2009), using one of the methods of analysis that will be described in Chapter 4. This was discussed further by McCombie et al. (2012).

3.6.2 Three-dimensional bulging

At its simplest level, a three-dimensional bulge can be just a two-dimensional bulge over a limited length of wall that may be weaker than adjacent sections.

Three-dimensional bulges seem to be more common than two- dimensional bulges, which is hardly surprising given the inevitable variability within any length of wall. They are often much more pronounced, while still being stable. However, a bulge that develops some time after a wall was built is likely to be a response to either a change in loading, whether externally applied or through water pressure changes, or to a deterioration in materi-als over many years. In such cases, although the bulge has clearly led to a new equilibrium being reached, the changes that led to its formation are likely to continue and could push the wall to the point where it can no lon-ger stand. This condition is likely to be precipitated by a single stone mov-ing slightly too far, so it tips over. Sometimes this results in a loss of a small part of the outer face of the wall, while the inner face continues to resist the earth pressure, and the rest of the face arches over where the missing material has fallen out. An apparently stable bulge could be on the point of reaching this condition and be highly dangerous; there is likely to be a void within the wall as the face has become separated from the stone behind it,

Figure 3.9 A well-developed bulge in a test wall. This bulge went on to collapse when the load plate on the backfill was pushed further.

and the facing stone could burst at any moment. This extreme behaviour has been observed in working walls, but was also seen in the test walls at Bath (Figure 3.9), which had been constructed with instrumentation so that these details of the behaviour could be confirmed.