Deformation and failure modes of drystone retaining

Powrie, W., Harkness, R. M., Zhang, X. & Bush, D. I. (2002). Geótechnique 52, No. 6, 435–446

Deformation and failure modes of drystone retaining walls W. P OW R I E , R . M . H A R K N E S S , X . Z H A N G ,y a n d D. I . B U S H { Dans cet expose´, nous cherchons les facteurs controˆlant la de´formation des murs de soute`nement en pierres se`ches au moyen d’analyses d’e´le´ments discrets. Nous montrons que les murs de soute`nement en pierres qui n’ont pas e´te´ exposeés au vieillissement climatique seront enclins a` basculer en se fragilisant, les flećhissements de la creˆte du mur ne de´passant pas 1% de la hauteur de remblayage, jusqu’a` ce que le facteur de sećurite´ (base´ sur la re´sistance du sol) tombe en dessous de 1·05. Une base de fondement compressible et le vieillissement climatique des blocs auront tendance a` re´duire la hauteur de remblayage au point de rupture a` un niveau infe´rieur a` celui indique´ par une analyse d’e´quilibre limite. Le bombement du mur sera probablement associe´ a` une de´te´rioration de la rigidite´ des joints entre blocs a` cause du vieillissement plutoˆt qu’a` une base de fondement compressible, bien que cette dernie`re diminue la perte de rigidite´ des joints, perte nećessaire pour causer le bombement. Le bombement est bien moins fragile que l’ećroulement et le proximite´ des murs bombe´s de la rupture pourrait, en certains cas, eˆtre e´valueé en fonction de la dimension du bombement.

In this paper, the factors controlling the deformation of drystone retaining walls are investigated by means of discrete element analyses. It is shown that toppling failure of unweathered drystone retaining walls is likely to occur in a brittle manner, with wall crest deflections not exceeding 1% of the backfill height until the factor of safety (based on soil strength) falls below 1·05. A compressible sub-base and weathering of the blocks will both tend to reduce the backfill height at failure to below that indicated by a limit equilibrium analysis. Bulging failure is more likely to be associated with a deterioration in block joint stiffness due to weathering than a compressible sub-base, although the latter will decrease the reduction in joint stiffness needed to cause bulging failure. Bulging is much less brittle than toppling, and the proximity to failure of bulging walls could in some circumstances be assessed on the basis of the size of the bulge.

KEYWORDS: numerical modelling and analysis; retaining walls; soil/structure interaction

BACKGROUND Masonry-faced retaining walls are common on highways throughout Europe, especially in hilly or mountainous regions. O’Reilly et al. (1999) estimate that there is a total length of between 120 and 140 km of masonry-faced walls on trunk roads in England and Wales, and perhaps of the order of 4000 km on principal and other routes. Many of these structures were built in the 19th and early 20th centuries, and typically consist of unbonded or drystone walls about 0·6 m thick. The stability of a drystone retaining wall is often assessed on the basis of a limit equilibrium analysis, with reference to a current design code. There is a perception, based (amongst other things) on the fact that the annual maintenance cost of masonry-faced trunk roads in England and Wales is less than 1% of the estimated replacement value (O’Reilly et al., 1999), that this approach tends to underestimate the stability of many such walls. If this is indeed the case, it is probably a result of the factors of safety specified by the design codes and/or the conservative selection of soil and geometrical parameters for analysis. Harkness et al. (2000) demonstrated that a simple limit equilibrium analysis can be used to give a close indication of the failure conditions for ideal drystone masonry walls having a rigid sub-base and unweathered blocks and joints, provided that the possibility of a failure surface that passes through the wall itself is admitted.

However, the extent to which deviations from the ideal, such as a variation in the angle of inclination of the joints, weathered stones, soft joints, and a compressible sub-base, might affect the stability of a drystone masonry retaining wall, perhaps leading to collapse at a height less than that indicated by a simple limit equilibrium analysis, remains unquantified. Conversely, in some cases a limited backfill zone between a masonry retaining wall and a stable rock face might be expected to lead to a greater degree of stability than a simple limit equilibrium analysis would suggest. Also, there is as yet little if any information relating the movement of a drystone wall to its factor of safety. In this paper, the factors controlling the mode of wall deformation, and the linkage between factor of safety and wall movement, are investigated by means of discrete element analyses of drystone masonry retaining walls of two different geometries. WALL GEOMETRIES AND MATERIALS PROPERTIES (BASELINE ANALYSES) The wall geometries studied in this paper are based on the two stable walls tested in Kingstown, Ireland (now Dun Laoghaire) in 1837 and reported by Burgoyne (1853). These walls were designated by Burgoyne (1853) as wall A and wall B. Wall A had a uniform thickness of 1·016 m (onesixth of the height) and was battered back at a slope of 1 in 5 (Fig. 1(a)); wall B had the same cross-sectional area but varied in thickness from 0·406 m at the top to 1·626 m at the base, with a vertical back (Fig. 1(b)). In both cases the masonry consisted of roughly squared granite blocks, laid dry (i.e. without mortar). The space behind each wall was backfilled with uncompacted earth, described by Burgoyne as ‘loose mould’. Its bulk density on placement was 1390 kg=m3 (87 lb=ft3 ), although this would probably have increased somewhat as the soil ‘imbibed the rain and the moisture readily’. As the

Manuscript received 15 November 2001; revised manuscript accepted 26 March 2002. Discussion on this paper closes 2 March 2003, for further details see p. ii. Department of Civil and Environmental Engineering, University of Southampton, UK. { Department of Earth Sciences and Engineering, Imperial College of Science, Technology and Medicine, London, UK. { Highways Agency, London, UK.

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POWRIE, HARKNESS, ZHANG AND BUSH

6·1 m (20 ft)

436

1m

1 m (3 ft 3 in)

10 m (32 ft 10 in)

6·1 m (20 ft)

(a)

1m

1 m (3 ft 3 in)

10 m (32 ft 10 in)

Deflection of masonry at the top: cm

(b) 8

6

4 Wall B 2

Wall A

0 4·2

4·4

4·6

4·8 5·0 5·2 5·4 5·6 Stable backfill height: m (c)

5·8

6·0

6·2

Fig. 1. Cross-sections of walls with inclined joints: (a) wall A; (b) wall B. (c) Comparison of wall deflections

soil was tipped loose, probably from wheelbarrows, it is also likely to have densified during construction activities. Also, the fact that the backfill was ‘kept to its full height from time to time as subsidence occurred’ indicates further densification. In the case of wall A, the masonry was built up as the backfill was placed, until the full height of 6·1 m (20 ft) was reached with no sign of distress. Wall B also stood following placement of the backfill to 6·1 m, although an outward movement at the top of 63 mm (2·5 in) occurred, together with some slight fissures in the face of the wall. Numerical analyses were carried out using the discrete element program UDEC (Universal Distinct Element Code: Itasca, 1993), reproducing as closely as possible the construction sequence adopted by Burgoyne. The masonry blocks in the wall, the natural bedrock and the soil backfill were all modelled as elastic/Mohr–Coulomb plastic materials. Each analysis was carried out in plane strain, with the bottom of the mesh below the rock base pinned to prevent movement in both the horizontal (x) and vertical ( y) directions. The right-hand vertical boundary (behind the natural

rock face) was prevented from moving horizontally, but was free to move in the vertical direction. In all of the analyses it was assumed that the pore water pressure throughout the backfill was zero at every stage. The basic numerical modelling procedure was described in detail in Harkness et al. (2000), and may be summarised as follows. In the analysis of wall A, the construction of the wall and the placement of backfill were simulated by adding wall and soil elements simultaneously. In the analysis of wall B, the wall was constructed in two stages of equal height in advance of the backfill. In both cases, the backfill was placed in lifts of 0·61 m (2 ft) up to 3·05 m (10 ft), and in lifts of 0·305 m (1 ft) thereafter—in both cases with further internal meshing to 0·15 m (0·5 ft) thickness. As a result of this procedure, some compaction occurs as subsequent soil layers are added, and friction begins to be mobilised on the sub-vertical faces of wall and quarry. The limiting effective soil/rock friction angle was that of the soil, whereas that of the wall joints and the wall/rock base was specified independently. The discrete element method uses a dynamic program in which each element is put in d’Alembert equilibrium at each time step. The timescale is an artifice of the analysis, and is referred to later in this paper as notional time. The time steps, and the consequent movement at each step, are both very small. The total number of time steps required for an analysis can run into millions, and a decision as to what constitutes failure is made on whether the deflection is levelling out or continuing to increase after a reasonable amount of wall deflection has occurred. This is illustrated by a plot of wall deflections (at different heights) against notional time, of the type shown in Fig. 10(c) of this paper (for a failing wall) and in Harkness et al. (2000) for all four of Burgoyne’s walls (two stable and two failing). Numerical analyses of all four of Burgoyne’s walls (including his walls C and D, which had different geometries and collapsed at a backfill height of 5·18 m or 17 ft), carried out by Harkness et al. (2000) using the material and interface stiffnesses given in Table 1, showed generally close agreement with the field observations. The parameters given in Table 1 were based on a qualitative geological assessment of the soils and rocks in the Dun Laoghaire area, the general data available in the literature, and Burgoyne’s own descriptions and observations as discussed in detail by Harkness et al. (2000). The backfill stiffness at every level was increased during backfilling in proportion to the weight of overlying material. The Harkness et al. (2000) analyses of stable walls A and B using the material parameters in Table 1 gave the stable deflections of the tops of the walls as a function of backfill height, as shown in Fig. 1(c). These analyses will be used as a basis for comparison for the results of the analyses presented in this paper, in which the effects of the following are investigated: (a) geometry (i) wall block corner rounding (ii) lateral extent of the backfill (iii) wall joint inclination (b) material properties (i) effective friction angle of the backfill (ii) effective friction angle and stiffness of the joints (iii) compressibility of the sub-base.

ROUNDED BLOCK CORNERS A large block corner radius might be viewed as simulating an effect of weathering, or may simply be a realistic representation of the blocks in many masonry retaining walls

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DRYSTONE RETAINING WALLS

437

Table 1. Material properties used in the UDEC analyses (see also Harkness et al., 2000) Granitey

Soil 1550

Bulk modulus: MPa

2650 (natural rock) 2270 (wall: Burgoyne, 1853) 22 000

Shear modulus: MPa

15 000

Property Mass density: kg=m

3

Tensile strength: MPa Shear strength at zero normal effective stress: MPa Effective angle of friction: (8) Joint shear stiffness: GPa=m thickness of the adjoining blocks Joint normal stiffness: GPa=m thickness of the adjoining blocks Joint tensile strength: MPa Joint friction angle: (8)

45 0·5

20–28 –

1

–

0 20–45

– –

Goodman (1980); Bandis et al. (1983); Cook (1992).

(a) the reduction of resisting moment due to the weight of the wall when the fulcrum is moved in from the toe of the wall by the amount of the corner rounding (Cooper, 1986)

10 Deflection of masonry at the top: cm

(Cooper, 1986). In the analyses described by Harkness et al. (2000) the masonry blocks from which the wall was constructed were given a nominal corner radius of 1 cm to avoid numerical problems. To examine the effect of increasing the degree of roundness of the block corners on wall movement and stability, new analyses have been carried out with block corner radii of 2·5 cm and 3·5 cm (Fig. 2). In these new analyses, a reduced backfill friction angle of 208 was used. This allowed comparisons to be made on the basis of both deflection behaviour and maximum stable backfill height since, even with 1 cm rounding, with the reduced backfill friction angle the walls would fail at a height of 6·1 m or less. A backfill height increment of 0·305 m (1 ft), as normally used both in this paper and by Harkness et al. (2000) for determining the maximum stable height of backfill, proved insufficient to distinguish the effect of block rounding for wall A: all three values of rounding led to failure at a backfill height of 5·79 m (19 ft). The analyses of wall A were therefore repeated with the backfill height increment decreased to 6 cm (0·2 ft). The maximum stable backfill height for 1 cm rounding determined in this way was 5·67 m (18·6 ft), and for 2·5 and 3·5 cm rounding 5·55 m (18·2 ft)—all with top-of-wall deflections of about 0·5% of wall height (Fig. 2(a)). For wall B, the increase in corner radius from 1 cm to 2·5 cm resulted in an increase from 6 cm to 10 cm in deflection at a backfill height of 5·49 m (18 ft). With a block corner radius of 3·5 cm the maximum stable height (using backfill increments of 0·305 m (1 ft)) was reduced from 5·49 m (18 ft) to 5·19 m (17 ft) (Fig. 2(b)), at which the deflection at the top of the wall was 2 cm. The generally larger maximum stable deflections obtained in the analyses of wall B indicate that this wall is less brittle than wall A. (The small maximum deflection calculated for wall B with a corner rounding of 3·5 cm is probably an artefact of the 0·305 m (1 ft) backfill height increments, and may for the purpose of this argument be discounted.) Two possible causes for the reduction of maximum stable height with increased block rounding are:

Masonry density = 2270 kg/m3 Friction angle of masonry joints = 45˚ Backfill friction angle = 20˚ Corner radius of masonry blocks = 1–3·5 cm Backfill density = 1550 kg/m3

8

6

4 1 cm 3·5 cm 2

2·5 cm

0 (a) 10 Deflection of masonry at the top: cm

y

1·5 7·5

1:0 þ 1:64z at depth z (z in m) 0:6 þ 0:98z at depth z (z in m) 0 0

2·5 cm

8

6

1 cm

4

3·5 cm

2

0 4·2

4·4

4·6

4·8 5·0 5·2 5·4 5·6 Stable backfill height: m (b)

5·8

6·0

6·2

Fig. 2. Effects of corner radius of masonry blocks on stability of (a) wall A, (b) wall B: reduced backfill friction angle of 208. Increments of backfill were 6 cm for wall A and 30 cm for wall B

(b) the effect on the mechanism of failure within the wall—allowing blocks to roll, for example, where they would otherwise have enough effective width or height to resist this tendency.


438


For wall A, the resisting moment due to the weight of the wall is reduced (compared with a 1 cm corner rounding) by 1·4% and 2·3% respectively for corner rounding of 2·5 cm and 3·5 cm. For wall B, the corresponding reductions are 1·6% and 2·7%. These changes, though small, would be sufficient to produce instability at a given backfill height if at that height the wall were only marginally stable. LATERAL EXTENT OF BACKFILL Burgoyne’s experiments were probably carried out in a quarry, with the result that the extent of the backfilled zone in the direction perpendicular to the wall was limited by the natural rock quarry face. Although in Burgoyne’s tests the extent of the backfill seems to have been sufficient not to influence the result, this may not apply to drystone walls in general. In reality the backfilled zone may be very narrow, so that the wall acts almost as a facing to the cut slope in the natural rock (Cooper, 1986; Wong and Ho, 1997). The effect of the extent of the backfill on wall stability was investigated using the geometry of wall A with a reduced backfill friction angle of 228. Four different backfill widths were investigated. The rock wall limiting the extent of the backfill was rough, and set back from the base of the wall by a ratio, R, of the maximum wall height (6·1 m). The wall was stable at a backfill height of 6·1 m (20 ft) when the ratio was small (R 0:33), but failed by overturning at a backfill height of 5·79 m (19 ft) with R 1:64. Figure 3(a) shows the deflection of the wall as a function of backfill height for different backfill widths. Reducing the backfill width reduces displacements and may increase the maximum stable height, partly as a result of friction at the vertical rock face helping to support the backfill and partly because of the increased constraint on the mechanism of failure in the soil. Figs 3(b) and 3(c) show the contours of horizontal displacement in the backfill during failure for R ¼ 0:52 and R ¼ 1:64 with backfill heights of 6·1 m (20 ft) and 5·79 m (19 ft) respectively. The practical implications of this are discussed later. JOINT INCLINATION Burgoyne’s walls A and B both had a 1 in 5 batter to the front face. As the blocks used to construct each wall were rectangular, construction of the walls with a planar (rather than stepped) front face meant that the block joints were similarly inclined at an angle of 11:38 (i.e. 1 in 5), except at the very bottom of the wall. Analyses have been carried out for each wall with both inclined and horizontal masonry joints, to investigate the influence of joint inclination on overall wall behaviour. The results for the baseline properties (458 joint friction angle, 288 soil friction angle and the stiffness moduli as given in Table 1) are shown in Fig. 4, and indicate very little effect of joint inclination for these joint and soil strengths. These results are part of a wider study in which both soil and joint friction were varied for the two joint inclinations, and are discussed later. EFFECTIVE FRICTION ANGLE OF THE BACKFILL Both wall A and wall B were stable at a backfill height of 6·1 m (20 ft) using the baseline parameters (Table 1) with a backfill friction angle of 288. A series of analyses was carried out for each wall in which the friction angle of the backfill was reduced in steps of 18 or 28 to 208 to explore the effect on wall movement and on the maximum backfill height that the wall could support. For each backfill friction angle a new analysis was carried out with the backfill built up in stages of 0·3 m (1 ft) until the wall failed or the full

Fig. 3. Effects of lateral extent of backfill on stability of wall A: (a) deflection with different ratios, R, of width to depth; (b) xdisplacement contours during failure with R 0:52, and (c) with R 1:64

backfill height of 6·1 m (20 ft) was achieved. The results for the two walls are given in Fig. 5, in which the deflection of the top of the wall is plotted against backfill height for all stable heights and all values of ö9. On the reasonable assumption that the active pressure of dry backfill against a wall is approximately proportional to depth, the total active force against the wall would be expected to be proportional to the square of the depth, whereas the moment of the force about its toe would be proportional to the depth cubed. Thus for a 5% reduction in backfill height from, say, 6·1 m (20 ft) to 5·79 m (19 ft), the active force against the wall would fall by about 10% and the moment of that force by about 14%. To increase the force or moment to their original values, the active pressure at the new backfill height would need to be increased by reducing the backfill friction angle. From an initial effective friction angle of 288, the required reductions in ö9 would be approximately 2:68 and 4:08 (to 25:48 and 248) for force and


1m

1 m (3 ft 3 in)

10 m (32 ft 10 in)


6·1 m (20 ft)


1m

1 m (3 ft 3 in)


6·1 m (20 ft)

(a)

Masonry density = 2270 kg/m3 Friction angle of masonry joints = 45˚ Backfill friction angle = 20–28˚ Corner radius of masonry blocks = 1 cm R (backfill width to backfill height) ≈ 1

8

6

25˚

2

26˚

20˚

27˚

24˚

28˚ 0 8

(a)

6

20–27˚ Will fail by overturning 28˚ Stable at 6·1 m

20˚

4

26˚

22˚ 27˚

28˚

24˚

2

0 4·4

4·6

(b) Deflection of masonry at the top: cm

22˚

20–24˚ Will fail by overturning 25–28˚ Stable at 6·1 m

4

4·2

10 m (32 ft 10 in)

439


5·8

6·0

6·2

Fig. 5. Effect of backfill friction angle on stability of (a) wall A, (b) wall B: inclined joints

8

6 Wall B

4

Wall A

2

0 4·2

4·4

4·6

4·8 5·0 5·2 5·4 5·6 Stable backfill height: m (c)

5·8

6·0

6·2

Fig. 4. Cross-sections of walls with horizontal joints: (a) wall A; (b) wall B. (c) Comparison of stability. Compare with Fig. 1 for inclined joints

moment respectively. Either of these reductions could be consistent with the results for changes in maximum stable backfill height given in Fig. 5, and the results do not therefore clearly distinguish between force and moment in causing failure. However, the mode of failure (by overturning) suggests that moment instability is the more likely cause. The brittleness of both walls is illustrated by the fact that, in all analyses leading to failure, any wall tilting more than 0:28—that is, a top deflection greater than about 2 cm or 0·3% of its height of 6·1 m (20 ft)—failed when subjected to a further 0·305 m (1 ft) of backfill. The converse appears to hold (except for the analyses in which a reduced extent of backfill was modelled) in that a wall with a deflection of less than 0·3% of its height was able to withstand a further 0·305 m increment of backfill. Furthermore, walls with the maximum computed stable deflection of 6 cm (1% of wall height) failed when the backfill friction angle was reduced by 18. A 18 reduction in backfill friction angle from 288 corresponds to a reduction in factor of safety (based on soil

strength) of approximately 1·04. Thus a wall with a factor of safety of just 1·04 may have deflected by only 1% of its height: this is discussed later. The results of a second series of analyses, similar to that described above but with horizontal and vertical joints, are shown in Fig. 6. The stability of the walls shows very little change from the results of the first series (that is, not discernible at the 0·305 m (1 ft) resolution of the backfill height changes), but for both walls the deflection at the top is rather less with horizontal joints than with inclined joints. This is probably because the mode of deformation of the former (at least, before failure) includes sliding on the joints: the mobilisation of active pressure by parallel outward movement of the wall requires less movement of the top of the wall than if the wall is constrained (by the resistance of the joints) to rotate about its base. The difference between the deformation patterns at failure is shown in Fig. 7 for wall B. Fig. 7(a) shows rotation (by a mechanism passing through the toe) for the wall with inclined joints, and Fig. 7(b) shows sliding on a joint near the base for the wall with horizontal joints. It is worth noting that relative sliding near the base of walls with horizontal joints would in reality be more noticeable than the top-of-wall deflection of either giving, perhaps, better warning of approaching instability. JOINT FRICTION ANGLE Analyses were carried out for both walls with both inclined and horizontal block joints, for a fixed backfill friction angle of 288 and block joint friction angles ranging from 208 to 458. The interface friction angle between the wall and the backfill remained at 288. For the walls with inclined joints, the results of these




8


440

8

Masonry density = 2270 kg/m3 Friction angle of masonry joints = 45˚ Backfill friction angle = 22˚ Corner radius of masonry blocks = 1 cm

Masonry density = 2270 kg/m3 Friction angle of masonry joints = 45˚ Backfill density = 1550 kg/m3 Backfill friction angle = 20–28˚ Corner radius of masonry blocks = 1 cm

–12 –10 –8 –6

6

–4

20–24˚ Will fail by overturning 25–28˚ Stable at 6·1 m

4

–2

22˚ 20˚ 21˚

2

25˚ 26˚ 27˚ 28˚

24˚

0 (a) (a)

20–27˚ Will fail by overturning 28˚ Stable at 6·1 m

6

20˚ kg/m3

4

28˚ 22˚ 24˚

2

Masonry density = 2270 Friction angle of masonry joints = 22˚ Backfill friction angle = 28˚ Corner radius of masonry blocks = 1 cm

–16

26˚ 27˚ –14 –12

0 4·2

4·4

4·6


5·8

6·0

–10

6·2

–8 –6 –4 –2

Fig. 6. Effect of backfill friction angle on stability of (a) wall A, (b) wall B: horizontal joints

analyses are shown in Fig. 8. Fig. 8(a) shows that, in the case of wall A, reducing the block interface friction angle from 458 to 268 had no significant effect on the deflection of the wall at a given backfill height. When the block joint friction angle was reduced (somewhat unrealistically) below 268, however, wall A failed by overturning and the maximum stable backfill height was reduced to 5·8 m (19 ft). The maximum stable backfill height then reduced by approximately 0·305 m (1 ft) for each 28 reduction in block joint friction angle below 268. For wall B with inclined joints (Fig. 8(b)), the apparent sensitivity to a reduction in block friction angle from 458 to 448 suggests that at a backfill height of 6·1 m (20 ft) this wall is only marginally stable. As the block joint friction angle was reduced towards 258, the wall displacement at a backfill height of 5·8 m (19 ft) increased very slightly, but overturning remained the dominant mode of deformation and failure. As the block joint friction angle was reduced below 258, the mode of deformation and failure changed to sliding. As with wall A with inclined joints, each 28 reduction in block joint friction angle below 258 reduced the last stable height by approximately 0·305 m (1 ft). With horizontal joints, both walls were stable at a backfill height of 6·1 m (20 ft) for joint friction angles between 248 and 458 (Fig. 9). Sliding occurred when the joint friction angle fell below 248 in both cases. For wall A, the maximum deflection at the top with a backfill height of 6·1 m (20 ft) was about 1·7 cm for all block joint friction angles between 248 and 458. For wall B, however, the maximum deflection at a backfill height of 20 ft increased from 3·7 cm to 6·7 cm as the block joint friction angle was decreased from 458 to 248. With a joint friction angle of less than 248, wall A slid along the base, whereas in the case of wall B sliding occurred along the base and also at the lower horizontal joints. In general, as the joint friction angle is reduced, there is a tendency for a wall with horizontal joints to perform better

(b)

Fig. 7. Comparison of internal failure deformation of wall B with different inclinations of joints within local areas around toe (see Figs 1(b) and 4(b): x-displacement contours (cm) and rotation of blocks. (a) inclined masonry joints; (b) horizontal masonry joints

than its counterpart with inclined joints, in terms of the maximum stable backfill height. This is probably a result of the different patterns of soil strain (and hence lateral stress distributions) implied by Fig. 7, which are in turn due to the increased opportunity for internal sliding deformation in the walls with horizontal joints. (Small changes in the backfill height due to settlements associated with different patterns of wall movement may also have had a significant effect on walls of marginal stability.) In extreme cases of low block joint friction (,248), the failure mode for wall A was changed from overturning to sliding by making the joints horizontal. WALL JOINT STIFFNESS Bulging is often encountered in ageing dry-stone retaining walls. It is an essentially flexible mode of deformation, in which the deformability of the wall is much greater than that of the individual masonry blocks. This suggests that the interfaces between the blocks may play an important role in bulging. A low friction angle between the blocks is likely to lead to sliding rather than bulging failure (see the earlier discussion and Cooper, 1986), indicating that bulging is likely to be associated with a reduction in block interface stiffness, rather than strength. Masonry blocks usually have roughly trimmed surfaces, resulting in a contact area between adjoining blocks of less than 10% of the total, even under high normal stresses



Fig. 8. Effect of friction angle of masonry joints on stability of (a) wall A, (b) wall B: inclined joints

Fig. 9. Effect of friction angle of masonry joints on stability of (a) wall A, (b) wall B: horizontal joints

(Goodman, 1976). Experimental measurements (Goodman, 1976; Bandis et al., 1983) show that rock surface stiffness is related to surface topography in addition to the materials properties of the rock blocks. Generally, a rough surface has

441

a low stiffness owing to the large deformability associated with the partial contact area. Furthermore, the surface stiffness is small at low normal effective stresses, and increases non-linearly with increasing normal stress (Cook, 1992). Real drystone walls are generally between 1·8 m and 10 m high (Cooper, 1986; Wong & Ho, 1997), giving average normal stresses between masonry blocks of less than 300 kPa. At these stresses, interblock stiffnesses would be expected to be relatively small. The stiffness and strength of the block interfaces could reduce over time as a result of weathering, stress-induced damage to the contact points, and possibly penetration of backfill material into the joints. The observation that walls can stand for long periods before collapsing suggests that collapse might be triggered by a time-related deterioration in the block interface properties. Analyses have therefore been carried out to investigate the effects of block surface (joint) stiffness on the stability of wall A. The backfill friction angle was taken as 288, and the materials parameters were as given in Table 1 with the reduced values of joint stiffness. In the baseline analyses, with joint normal and shear stiffnesses of 1000 and 500 MPa=m respectively, wall A was stable at a backfill height of 6·1 m (20 ft). With the normal stiffness reduced to 60 MPa=m and the shear stiffness to 30 MPa/m, stable bulging developed at a backfill height of 5·8 m (19 ft). These stiffnesses represent a 17-fold reduction in the original values. Bulging is indicated by the fact that the largest displacement occurred in the lower section of the wall, as shown in Figs 10(a) and (c). Increasing the backfill height to 6·1 m (20 ft) caused the wall to topple (Fig. 10(b)). The transition from bulging to toppling at a backfill height of 6·1 m is indicated in the graph of displacement against notional time (Fig. 10(c)) by the crossing over of the displacement traces. The introduction of soft joints between the masonry blocks elicited a more flexible response from the wall than in the baseline analyses. Although bulging did occur, and was at its most severe prior to failure, the mode of collapse was still ultimately toppling. The introduction of soft joints reduced the maximum stable backfill height from more than 6·1 m (20 ft) to 5·8 m (19 ft). One further analysis was carried out, in which the joint stiffnesses and joint strengths of wall A at an initially stable backfill height of 5·8 m (19 ft) were gradually reduced from 60 MPa=m to 1 MPa=m (normal stiffness), 30 MPa=m to 0:5 MPa=m (shear stiffness) and 458 to 288 (strength). The reduction in stiffness resulted in the growth of the bulge in the wall, and eventually failure occurred by bulging at a backfill height of 5·8 m (Fig. 11). The very low values of joint stiffness that had to be invoked to promote bulging failure help to explain the observation made by Cooper (1986), that ‘bulging failures on truly rigid bases appear rare, except where weathering of the lower part of the face has increased the compressibility dramatically in the zone of negative eccentricity’—that is, where a bulge causes the line of thrust down through the wall to pass close to the back of the bulged section, increasing the stresses on the weakened material. COMPRESSIBILITY AND STRENGTH OF THE SUB-BASE The potential importance of a compressible or weak subbase in the development of a bulging failure in a drystone retaining wall is highlighted by Cooper (1986). To investigate the effects of sub-base compressibility and strength, analyses were carried out for walls A and B using the baseline parameters, but with the different sub-base stiffnesses



442 Max. displacement = 2·0 cm

0

5 cm

(a)

0

Fig. 11. Wall deformation and backfill failure zones due to bulging failure of the wall in Fig. 10(a), resulting from gradually reduced joint stiffness and joint strength

20 cm

Displacement (cm) (outwards is negative)

(b) 5·79 m

Backfill height 6·1 m

0 –1 –2 –3 2 m above base

–4 –5

4 m above base –6 –7

At the top 0

2

4

6 8 Notional time (c)

10

12

14

Fig. 10. Displacements of wall A with soft joints at (a) stable backfill height of 5·79 m; (b) unstable backfill height of 6·1 m; (c) deflection history

and strengths shown in Table 2. The sub-base in the vicinity of the wall and the lower blocks of the wall are meshed to 0·1 m (as detailed in Harkness et al., 2000) to provide adequate resolution for yielding and deformation. The various sub-base parameters are representative of materials ranging from hard rock to medium sand, any of which might be used as a foundation in practice (Bowles, 1977; Goodman, 1980).§ § It is recognised that the thickness of the sub-base (between the wall and the rigid bottom boundary) is limited. The compressibility of the sub-base will depend on its thickness as well as on its stiffness. The use of a thicker sub-base layer in the mesh would therefore probably have given quantitatively, if not qualitatively, different results.

The results of the analyses with non-rigid sub-bases are summarised in Table 3. They show that sub-base compressibility or bearing capacity failure might occur when the wall is founded on anything softer or weaker than rock (Figs 12(a) and (b): the plasticity indicators in the figures show that the Mohr–Coulomb yield condition has been reached). With stiffness and strength parameters representative of a very soft rock, deformation of the sub-base still led to the collapse of the wall even though the sub-base itself did not suffer a bearing capacity failure (Table 3). This confirms the need to distinguish between wall collapse arising from tilting due to the compressibility or localised failure of the part of the sub-base under the toe of the wall, and wall collapse due to a general bearing capacity failure, as recognised by Cooper (1986). Wall collapse resulting from bearing capacity failure or excessive sub-base compressibility was always by toppling or sliding. It was not possible to promote bulging failure, or even significant bulging deformation, simply by reducing the strength and stiffness of the sub-base. This suggests that bearing capacity failure or compressibility of the sub-base is unlikely to be the sole cause of wall bulging. However, it is possible that the effects of foundation compressibility or bearing failure combined with a reduction in the block interface stiffness within the wall could promote bulging failure: this is investigated below. With a softer and weaker sub-base (i.e. sand), large movements of the foundation started to occur at a lower backfill height for wall A than for wall B. This is not surprising, given the smaller base width of wall A. However, wall A stabilised following a degree of deformation, resulting in a greater stable backfill height for wall A than for wall B, but with a larger deflection (Table 3). This may be consistent with a greater restoring moment due to friction on the back of the wall in the case of wall A than wall B, as discussed in a later section. Bearing failure could in reality be prevented or postponed by the provision of a wider foundation block where the sub-base material is of reduced strength or stiffness. EFFECT OF A REDUCED WALL JOINT STIFFNESS AND A COMPRESSIBLE SUB-BASE A series of analyses was carried out using the geometry of wall A to investigate the combined effects of a reduction



443

Table 2. Parameters used in further analysis of non-rigid sub-bases Hard rock Density: kg=m3 Bulk modulus: MPa Shear modulus: MPa Cohesion: MPa Friction angle: 8 Tensile strength: MPa Interface between masonry and sub-base Normal stiffness: MPa=m Shear stiffness: MPa=m

Medium rock

Very soft rock

Dense sand

Medium sand

2650 22 000 15 000 7·5 45 1·5

2650 2200 1500 5 30 1

2500 100 60 0·5 30 0·1

2000 50 30 0 35 0

2000 25 15 0 30 0

30 000 10 000

3000 1000

200 120

100 60

67 40

These parameters represent a wide range of rock and soil properties. The specific ground types suggested are indicative only (Bowles 1977, Goodman 1980).

Table 3. Deformation and stability of walls A and B with different sub-base properties Wall

Stable height: m; ft A

Hard rock Medium rock Very soft rock Dense sand Medium sand

6·1; 6·1; 5·8; 5·49; 4·88;

Deflection: cm

B 20 20 19 18 16

6·1; 6·1; 5·8; 5·19; 4·58;

20 20 19 17 15

Wall rotation Failure mode

A

B

A

B

A

B

1·12 1·25 2·16 6·83 18·1

1·94 2·0 2·63 3·69 3·35

F F F F B

F F F F F

S S Fw Fb Fb

S S Fw Fb Fb

F, forward rotation of wall; B, backward rotation of wall; S, stable; Fw , failure in wall; Fb , failure in base.

in block joint stiffness and construction on a softer/weaker sub-base. The combinations of joint stiffness and sub-base stiffness and strength investigated, and the results of the analyses, are summarised in Table 4. These results indicate that the interaction of joint weathering and sub-base compressibility/strength is quite complex. They suggest that on a firm sub-base (very soft rock), a reduction in joint stiffness may not always have a detrimental effect on wall stability. While the initial reduction in joint stiffness led to a reduction in the maximum stable height from 6·1 m (20 ft) to 5·8 m (19 ft), further reductions in joint stiffness actually resulted in a restoration of the maximum stable height to 6·1 m (20 ft). This confirms that bulging can act to help stabilise a wall, for the reasons discussed below. In contrast, on the dense sand sub-base (which consistently exhibited bearing capacity failure), progressive softening of the joints led to a monotonic decrease in the maximum stable height. As noted previously, the wall with hard joints failed by toppling. On softening the joints, the mode of wall failure changed from toppling to moving out at the base (as a result of bulging) combined with bearing failure of the sub-base. DISCUSSION AND IMPLICATIONS FOR PRACTICE The results reported in this paper go some way towards explaining the perception that the application of a conventional design code to a drystone retaining wall leads to an over-conservative assessment of its stability. First, although the failure by toppling of a wall with sound foundations and unweathered blocks may be well predicted by a conventional limit equilibrium analysis (Harkness et al., 2000), toppling deformations remain small (less than 1% of wall height) until the factor of safety on soil strength falls below about 1·05. In other words, these walls can perform satisfactorily

(in terms of displacements) at factors of safety considerably below those required by a modern design code. This is consistent with the statement made by Cooper (1986) that ‘it is unusual to find walls with large pre-failure deformations due to toppling’. It should also come as no surprise in view of Terzaghi’s observation, based on tests on large retaining walls, that a deflection of 1% of the wall height is normally enough to bring a dry sand backfill to the active state (Terzaghi, 1934; 1936). Second, the results of the numerical analyses (in terms of both displacements and the maximum stable backfill height) were very sensitive to the frictional strength (ö9) of the backfill. Underestimating the backfill friction angle by as little as 18 could lead to the underestimation of the factor of safety on soil strength by 4%: the uncertainty involved in selecting parameters for the back-analysis of an existing wall is likely to be rather greater than this. Third, many drystone retaining walls, particularly in hilly and mountainous areas, act primarily as facings, with a relatively narrow backfilled zone occupying the space between the wall and a steep, stable cut face (O’Reilly et al., 1999). In these circumstances, the reduced backfill width will reduce displacements and may increase the maximum stable height, probably as a result of friction at the vertical rock face helping to support the backfill. One potential problem with a narrow backfill between a wall and a lowpermeability natural rock face is that the relatively small voidage could allow pore water pressures to build up very rapidly in the event of flooding from the retained surface, especially if the backfill is not well drained (Wong & Ho, 1997). In contrast to the brittle nature of toppling failure, quite large bulging deformations can be sustained with the wall apparently remaining stable (Cooper, 1986). In the numerical analyses described in this paper, bulging was always associated with a reduction in block joint stiffness. A weak or



444 Property Mass density: kg/m3 Friction: ˚ Shear modulus: MPa Bulk modulus: MPa Joint shear stiffness: MPa/m Joint normal stiffness: MPa/m Joint friction: degree

Masonry 2270 45 1500 2200 500 1000 45

Backfill 1550 28 (see Table 1) (see Table 1) – – –

Base 2000 35 30 50 – – –

(a)

(b)

Fig. 12. Failure zones of (a) wall A, (b) wall B, standing on a soft base: shear failure

compressible sub-base might lead to a reduction in the maximum stable backfill height, but did not alter the mode of deformation and failure from toppling (or sliding if the block joint friction angle was low). In practical terms, bulging failure is easier to identify and possibly prevent, as it is much less brittle than toppling: it is unlikely that incipient toppling failure will be detected from intermittent observations of wall movement. The potentially beneficial effects of bulging on wall stability are illustrated by the analyses of wall A on a firm sub-base, in which a reduction in joint stiffness increased the maximum stable height by allowing increased bulging to take place. In practice, progressive bulging over time could occur as a result of a reduction in block interface stiffness due to weathering. In considering the reasons for wall collapse due to overturning or bulging, the structure of the wall is of critical importance. Points of high contact stress between blocks will suffer more deformation due to ageing and weathering than contacts carrying little or no stress. For a wall formed from

well-trimmed blocks, the contact deformation required before a good seating is achieved and the load stabilises could be modest. This will result in a block joint behaviour that is relatively stiff and gives little opportunity for wall deformation. On the other hand, in a wall formed from untrimmed blocks, even though hand-selected by an experienced drystone waller, the points of contact are likely to be fewer and further between. In this case, considerable deformation may be required before there is an appreciable redistribution of load, allowing not only softer joint behaviour but also some rotation of the blocks before a new, firmer seating is established. In the latter case the wall can deform relatively easily and bulging is possible, whereas for the stiffer wall even tilting of the base blocks due to foundation movement (which might otherwise be expected to promote bulging) leads only to tilting of the whole wall. A second important factor is the mode of deformation of the backfill in relation to wall movement. For a wall that rotates about its base, the friction on the back face of the wall might be fully mobilised near its top as the backfill moves out and down behind the wall, but at intermediate heights the downward movement of the backfill is reduced and may be insufficient to mobilise the full soil friction value. The total frictional force acting downwards on the back face of the wall, which imparts a stabilising moment to the wall, may not then reach the value calculated on the basis of the uniform mobilisation of full soil/wall friction over the whole depth of the wall. On the other hand, if the wall moves outward without rotating—as the result either of a local bulge or of sliding on a horizontal joint near the base—the backfill could reasonably be expected to deform as a sliding wedge and thus mobilise friction over the full height of the wall. For relatively inflexible walls on a soft base, this difference in behaviour is shown in Fig.12. Behind wall A, the soil fails as a sliding wedge without rotation, mobilising full wall friction at all levels. Wall B rotates outward as a result of compression of the sub-base under the toe, and full wall friction is mobilised progressively from the top of the wall. Finally, it may be noted that, in reality, bulging on plan associated with three-dimensional effects could lead to larger stable deformations than indicated by the two-dimensional analyses reported in this paper. This is a subject of further investigation.

CONCLUSIONS For drystone masonry retaining walls in which deformation and failure occur in conditions of plane strain, the analyses presented and discussed in this paper have shown the following: (a) For an ideal wall that is unweathered with a rigid subbase, failure is likely to occur by toppling, with wall crest deflections not exceeding 1% of the backfill height until the factor of safety (based on soil strength) falls below 1·05. This means that a wall in danger of failure by toppling would be difficult to detect from the measurement of wall displacement alone. (b) Reducing the width of backfill between a wall and a steep, stable natural rock face reduces displacements and may increase the maximum stable height, probably as a result of friction at the rock face helping to support the backfill. However, such a backfill must be well drained to avoid the possibility of a rapid rise in pore water pressures due to flooding from the retained soil surface. (c) At low inter-block friction angles, walls with battered front faces and horizontal joints moved less at the top



445

Table 4. Combined effects of sub-base and joint stiffness on deformation behaviour of wall A Joint stiffness (normal/shear), MPa=m

Hard joints

Medium joints

Soft joints

Very soft joints

100/500

200/100

100/50

60/30

On hard rock Highest stable height: m; ft Maximum stable deflection: cm Position of maximum stable deflection Position of maximum unstable deflection wall Direction of rotation of wall Failure mode

6·1; 20 0·2 Top of wall – Backward Stable

5·8; 19 5·8; 19 5·8; 19 0·2 1·1 2·1 2 m above base of wall 2 m above base of wall 2 m above base of wall Top of wall Top of wall – Backward Backward Backward Toppling Toppling Toppling

On very soft rock Highest stable height: m; ft Maximum stable deflection: cm Position of maximum stable deflection Position of maximum unstable deflection Direction of rotation of wall Failure mode

6·1; 20 2·9 Top of wall – Forward Stable

6·1; 19 6·1; 20 6·1; 20 0·4 1·4 2·9 2 m above base of wall 2 m above base of wall 2 m above base of wall – – – Backward then Forward Backward then Forward Backward then Forward Bulging Stable Stable

On dense sand Highest stable height: m; ft Maximum stable deflection: cm Position of maximum stable deflection Position of maximum unstable deflection Direction of rotation of wall Failure mode

5·49; 18 3·7 4 m above base 4 m above base Forward Failure in base

5·49; 18 5·19; 17 5·19; 17 2·4 1·7 2·6 2 m above base of wall 2 m above base of wall 2 m above base of wall 2 m above base of wall 2 m above base of wall 2 m above base of wall Backward then Forward Backward then Forward Backward then Forward Failure in base Failure in base Failure in base and bulging and bulging and bulging

of the wall than similar walls with inclined joints (i.e. normal to the front face of the wall), though ultimate failure for both walls occurred at the same soil friction angles. Walls with horizontal joints had the possible advantage that movement at the base of the wall prior to failure could give a warning of incipient instability whereas the very small movement of the top of the wall for both walls could be regarded as insignificant. However, at inter-block friction angles likely to be encountered in practice (~ 458) there was little if any significant impact. (d ) A real drystone wall is likely to have a non-rigid subbase and weathered blocks. Both of these will tend to reduce the backfill height at failure to below that indicated by a limit equilibrium analysis—by between 20% and 25% for the two walls investigated in this study on a sub-base representative of a medium sand. The only circumstance in which a simple limit equilibrium analysis is likely to underestimate the backfill height at failure (by 5% in this study) is when the wall acts essentially as a facing, with only a limited backfill zone between it and a stable rock face. (e) Weathered blocks were simulated by increasing the degree of block corner rounding and reducing either the strength or the stiffness of the joints. Increasing the degree of block corner rounding may have an adverse impact on a wall already of marginal stability: in the case of wall A, an increase in the degree of corner rounding reduced both the maximum stable displacement and the backfill height at failure. However, it did not alter the mechanism of wall failure, which remained by toppling. ( f ) A large reduction in joint strength was needed to have a significant impact on wall stability: the mechanism of wall failure then changed from toppling to sliding. Wall bulging could be achieved only by reducing the joint stiffness. A substantial reduction in joint stiffness was needed to cause bulging failure, which could be made to occur at a lower backfill height than that at which a limit equilibrium analysis would suggest failure by toppling.

(g) A reduction in sub-base strength and stiffness may cause failure of the wall at a lower backfill height than a simple limit equilibrium analysis would suggest. With a weaker and more compressible sub-base, but reasonably stiff wall joints, failure would still be by toppling—precipitated either by bearing capacity failure or by the compression of the sub-base beneath the toe. Wall bulging is unlikely to occur solely as a result of the deformation of the sub-base, but the reduction in joint stiffness needed to cause bulging failure decreases with the stiffness and strength of the sub-base.

ACKNOWLEDGEMENTS The work described in this paper was carried out in the Department of Civil and Environmental Engineering at the University of Southampton, under contract to the Highways Agency. The views expressed are those of the authors, not the Highways Agency. The authors are grateful to Drs K. C. Brady, M. R. Cooper and M. P. O’Reilly for helpful discussions and advice.

NOTATION R ratio of backfill width to overall wall height x horizontal distance y, z depth ö9 effective backfill friction angle REFERENCES Bandis, S. C., Lumsden, A. C. & Barton, N. R. (1983). Fundamentals of rock joint deformation. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 20, 249–268. Bowles, J. E. (1977). Foundation analysis and design, 2nd edn. New York: McGraw-Hill. Burgoyne, J. F. (1853). Revetments or retaining walls. Corp of Royal Engineers Papers 3, 154–159. Cook, N. G. W. (1992). Natural joints in rock: mechanical, hydraulic and seismic behaviour and properties under normal stress. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 29, 198–223.


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2·0: User’s manual. Minneapolis: Itasca Consulting Group Inc. O’Reilly, M. P., Bush, D. I., Brady, K. C. & Powrie, W. (1999). The stability of drystone retaining walls on highways. Proc. Instn Civ. Engrs (Municipal Engineer) 133, 101–107. Terzaghi, K. (1934). Large retaining-wall tests I–V. Engng News Rec. 112, No 10, 316–318. Terzaghi, K. (1936). A fundamental fallacy in earth pressure computations. J. Boston Soc. Civ. Engrs, 23, 71–88. Wong, H. N. & Ho, K. K. S. (1997). The 23 July 1994 landslide at Kwun Lung Lau, Hong Kong. Can. Geotech. J. 34, 825–840.
