Roc~anciors-s:a:eo':iear:

~ar:: 3esicn'y G. S. LITTLEJOHN", BSc, PhD, MICE, MIStructE, FGS, and D. A. BRUCE", BSc,AMICE, FGS

BOND BETWEEN CEMENT GROUT 3. Mechanical interlock. This is similar to e.g. 1.0mm off-set, 40mm pitch, a bond AND STEEL TENDON micro mechanical locking, but on a much length of 65 diameters may be assumed for larger scale, as the shear strength of the the above conditions. Introduction grout is mobilised against major tendon (iii) Galvanised wire provides a poor Little attention has been to this paid irregularities, e.g. ribs, twists. bond, less than half that of comparable of rock anchor aspect design, principally An idealised representation of these plain wire. because engineers usually consider that three major bond components is shown in It may be assumed that 80 cent the fixed anchor length chosen with re- (iv) per Fig. 14. For short embedment lengths the of the maximum stress is developed in a spect to the rock/grout bond ensures adhesive component is most important, but of 70 diameters for the conditions more than adequate tendon embedment length mentioned in and in a length of 54 dia- length. (i) Lu meters for the conditions mentioned in However, as has been demonstrated in (ii). Strand the section dealing with rock/grout bondfi, little standardisation or uniformity of ap- l- R (i) From the available experimental data, Lrt proach is apparent related to the grout/ AL INTERLOCK) the transmission length for small diameter tn ordinary strand is not proportional the tendon bond, and the rather simple design Lu to LZ diameter the assumptions commonly made are in contra- of tendon. Table Vll gives diction to certain experimental observa- values of transmission length for strand tions. working at an initial stress of 70 per cent o ultimate in In this section, the mechanisms of bond ADHESION concrete of strength 34.5-48.3 are discussed and anchor design pro- N/mm'. cedures employed in practice are re- SLIP TABLE VII TRANSMISSION LENGTHS viewed. Bearing in mind the scarcity of — Idealised representation major information pertaining to anchors, data Fig. 14. of FOR SMALL DIAMETER STRAND components of bond abstracted largely from the fields of re- Transmission length inforced and prestressed concrete are also Diameter of are also presented, which relate to the for longer lengths, all three may operate— strand (mm j (mm) (diameters failure initially the j magnitude and distribution of bond. adhesion occurring at proximal end and then moving progres- 9.3 200 (m25) 19-24 sively distally to be replaced by friction The mechanisms of bond and/or mechanical interlock. Frictional and 12.5 330 (~25) 25-28 It is widely accepted that there are three lat- mechanisms: interlocking resistances increase with 18.0 500 (~50) 25-31 eral compression and decrease with lateral 1. Adhesion. This provides the initial tension. the shear strength N.B.—Range of results given in brackets. "bond" before slip, and arises mainly from Clearly, grout and the nature of the tendon surface, both the physical interlocking (i.e. gluing) of the micro-and macroscopically, are major fac- (ii) Tests in concrete of strength 41.4- microscopically rough steel and the sur- tors in determining bond characteristics. 48.3N/mm'ith Dyform compact strand rounding grout (Fig. 13). Molecular attrac- at 70 per cent ultimate show an average Fixed anchor design transmission length of 30-36 diameters. CEMENT GROUT It is common in practice to find embed- According to the results of an FIP ment lengths for bars, wires and strands questionnaire (1974) national specifica- quoted as equivalent to a certain number tions vary considerably for transmission of diameters, as this method ensures a lengths, the most optimistic being those of maximum value of apparent average bond the United Kingdom. It is accepted that stress for each type of tendon. The trans- compact strand e.g. Dyform, has transmis- STEEL BAR OR WIRE TENDON mission length is the length required to sion lengths 25 per cent greater than those for normal 7-wire strand, and that sudden Magnified view of interface transmit the initial prestressing force in a Fig. 13. con- release of load also increases the trans- between grout and steel tendon to the surrounding grout or crete. mission length. (An additional 25 per cent In Britain, the following general recom- is recommended in Rumania). tion is also thought to act. Adhesion is con- mendations may be followed, based on Bar sidered to disappear when slip comparable CP 110, 1972 and information supplied by (i) With regard to permissible bond with the size of the micro indentations on Bridon Wire Ltd (1968). stresses for single plain and deformed bars the steel occurs. Wire in concrete, Table Vill illustrates the 2. Friction. This component depends on (i) For a bright or rusted, plain or inden- values stipulated by the British Code for confining pressure, the surface charac- the ted wire with a small off-set crimp e.g. different grades of concrete. These values and the amount of teristics of the steel, 0.3mm off-set, 40mm pitch, a transmission are applied to neat cement grouts on occa- slip, but is largely independent of the mag- length of 100 diameters may be assumed sions. nitude of the tendon stress. The pheno- when the cube strength of the concrete or (ii) For a group of bars, the effective mena of dilatancy and wedge action also grout at transfer is not less than 35N/mm'. perimeter of the individual bars is multi- contribute to this frictional resistance as (ii) For a wire of a considerable crimp plied by the reduction factors overleaf. radial strains are mobilised where the lofrg- itudinal strain changes. TABLE VIII—ULTIMATE ANCHORAGE BOND STRESSES s Geotechnics Research Group, Engineering Dept. Characteristic strength of concrete N/mms) Marischal College, University of Aberdeen (fr„, Ii This is the second section of this article on rock Type of anchor design; the first which appeared in our 20 25 30 Msy issue, pp 25-32, gave an introduction to the bar subject and dealt with uplift capacity of. the Maximum bond stress, rock anchor system, and the bond between N/mm'.4 cement grout and rock. These two articles re- present the first of a three-part series that pro- Plain 1.2 1.9 vides a state-of-the-art review of rock anchors, covering design, construction, and testing and ~fermed 1.7 1.9 2.2 2.6 stressing. July, 1975 41 No. of barsin group Reduction factor stand about 156-178kN with 0.6m embed- and wires with grout. The value of the bond 2 0.8 ment. Since the capacity of such strand (up to 0.88N/mm') for 15.2mm strand is 3 0.6 is usually in the range 178-270kN, Golder slightly higher overall than that for 12.7mm 4 0.4 Brawner Assocs. conclude that no strand strand (up to 0.72N/mm'), and in both of a rock anchor logically needs an embed- cases there is a trend towards a reduction It is important to note that no information ment length in excess of 1.5m. However, of the bond with an increase in number of is provided in the Code on group geometry for other reasons, a length of 3m is usually strands. e.g. minimum spacing, where the reduction considered the minimum acceptable. (ii) The actual safety factor against fail- factors should be employed. In addition no Data abstracted from papers describing ure of the grout/tendon bond is usually guidance of any kind is given for groups rock anchor contracts is presented in well in excess of 2. of strands or wires. Tables IX, X and XI for bar, wire and (iii) The average bond developed by With reference to minimum embedment strand, respectively. In all the calculations, bars, especially deformed types, is on aver- lengths, Morris and Garret (1956) have except where otherwise noted, the bond is age significantly higher than that developed calculated from stressing tests on 5mm dia- assumed uniform over the whole tendon by strands or wires. Also the presence of meter wires that the minimum necessary embedment zone, which is taken as equal deformities increases the bond magnitude embedment is just over 1m. Golder Braw- to the length of the fixed anchor. by up to 2 times with respect to plain bars. ner Assocs. (1973) found that although the Bearing in mind the relatively small num- grout/strand bond is higher than expected ber of values, comments are limited to the Distribution of bond from tests on single wires due to "spiral following: Much of the work to investigate the dis- interlock", the value drops rapidly if the (i) There would appear to be a greater tribution of bond along grout/steel inter- embedment length is less than 0.6m. Re- degree of uniformity on values chosen for faces has been carried out in the United sults from Freyssinet anchors with spacers the working bond between strand and States in connection with prestressed and- have shown that each strand can with- grout, than for the bond developed by bars reinforced concrete. Gilkey, Chamberlin

TABLE IX—GROUT/BAR BOND VALUES WHICH HAVE BEEN EMPLOYED OR RECOMMENDED IN PRACTICE Working Test Ultimate Embedment Load load bond bond Bar tendon (m) (kN) (N/mmt) (N/mmt) (N/mmr) Remarks Source Plain 1.2-1.9 Design criteria: bond dependent Britain —CP110(1972) Deformed 1.7-2.6 on concrete Square twist 5.25 Design criteria Britain —Roberts (1970) Ribbed 7.0 Plain 1.38 Short embedment test Canada —Brown (1970) Plain and threaded end 2.62 Bond dependent on embedment and grout tensile stress Deformed bar 30d Design criteria: "solid" rock Canada —Ontario Hydro (1972) Deformed bar 40d + Design criteria: "seamy" rock 20 No. 20mm dia plain 2.5 1750 0.56 Test anchor Italy —Berardi (1960) 20mm dia ribbed and threaded 2.2 1.1 Test anchor Italy —Beomonte (1961) with end nut 3.9 0.6 Test anchor 2.2 1.2 Test anchor 2.2 0.9 Test anchor 25mm dia deformed bar 0.2 2.7 Test anchor Canada —Brown (1970) 0.4 5.0 Test anchor, Bond for deformed 0.6 bar=5 x bond for plain bar 25.4mm dia square 1.83 289 1.98 Test anchor USA—Salisman & Schaefer (1968) 25.4mm dis plain 0.06 52 10.1 Tests: for each pair the first Australia —Pander et al (1963) 0.06 53.5 11.2 test conducted at 28 days, 0.12 52 5.5 and the second at 90 days 0.12 67 7.0 0.18 63 4.4 0.18 117 8.1 0.36 139 4.9 0.36- 148 5.1 28mm dis plain 5.9 160 0.31 Test anchor: bond known to be Italy —Berardi (1967) 11.0 160 0.16 much higher locally 28 mm dis plain 400 0.76 Design criteria Switzerland —Comte (1971) 28.6mm dia plain 0.91 220 2.72 Test anchor USA —Drossel (1970) 30mm dia plain 320 3.0 7.2 Test at bar UTS Switzerland —Muller(1986) 31.8mm dia high tensile 1.83 605 3.3 Commercial anchor USA —Wosser et el (1970) 31.8mm dia and thread 1.2 700 5.74 Test anchor USA —Drossel (1970) 31.8mm dia Dywidag & locknut 8.5 545 0.64 Commercial anchor USA —Oosterbaan et al (1972) 35mm dia mild steel 6.1 360 0.54 Anchor pile Canada —Jaspar et al (1969) 35mm dia plain 6.1 505 0.75 Test anchor Canada —Barron et al (1971) 35mm dia plain 6 700 1.06 Commercial anchor USA—Feld et al (1974) 43mm dia mild steel 12.2 610 0.37 Anchor pile Canada —Jasper et al (1969) 44mm dia plain 0.35 4.7 Test anchor Canada —Brown (1970) 0.6

TABLE X—GROUT/WIRE BOND VALUES WHICH HAVE BEEN EMPLOYED OR RECOMMENDED IN PRACTICE Working Ultimate Embedment Load bond Test bond bond Wire tendon (m) (kN) (N/mmt) (N/mm') (N/mmr) Remarks Source Plain 100d Design cntena Britain —CP110 (1972) also Crimped 65d CP115 (1969) Groups of 5, 6, 7mm 0.5-1.0 Design criteria Switzerland —Comte (1971) e.g. from 14 No. 5mm 1.7-3.4 350 to 54 No. 7mm 6-12 2470 Plain/Crimped H 1.035 Design criteria Australia —Standard CA 35 (1973) 12 No. 5mm 1.8 280 0.53 Commercial anchor Switzerland —Pliskin (1965) 24 No. Smm 4.0 500 0.33 Commercial anchor Poland —Buiak et al (1967) 37 No. 5mm 1.0 1540 2.62 Test anchor Britain —Morris et al (1956) 2.44 700 0.49 Commercial anchor 2.44 950 0.67 Commercial anchor 40 No. Smm 5.0 850 0.27 Commercial anchor Switzerland —Birkenmaier (1953) 102 No. 5mm 4.0 2000 0.32 Commercial anchor India —Rao (1964) 24 No. 6.4mm 18.3 670 0.076 Commercial anchor USA —Reti 1964) 90 No. 6.4mm HT 9.14 3750 0.23 Commercial anchor USA—Thompson (1970) 90 No. 6.4mm 9.14 11570 0.70 Commercial anchor Canada —Golder Brswner (1973) 12 No. 7mm 2.5 515 0.78 Commercial anchor Switzerland —Pliskin (1965) 12 No. 7mm 7.5 450 0.23 Commercial anchor Brazil —ds Costa Nunes (1969) 12 No. 7mm 2.5 600 0.93 Commercial anchor Africa —Anon (1970) 12 No. 7mm 443 500 0.47 Commercial anchor Italy —Berardi (1972) 34 No. 7mm 7.6 130:I 0.23 Commercial anchor Australia —Rawlings (1968) 35 No. 7mm 3.5 1383 0.51 Commercial anchor Switzerland —Ruttner (1966) 0.6 2.26 Test anchor 1.5 2.0 Test anchor 72 No. 7mm galvanised HT 5.2 2740 0.33 Commercial anchor Australia —Maddox et el (1967) 33 No. 7.62mm 3.5 1700 0.62 Commercial anchor Germany —Anon (1972) 12 No. smm 2.9 675 0.77 Commercial anchor Switzerland —Pliskin (1965) 12 No. Bmm 0.47 Test anchor Britain —Bundred (1973) 18 No. 8mm 1450 0.7 Test anchor: Switzerland —Walther (1959) 27 No. Bmm 225n 0.7 at wire UTS 24 No. smm 4.5 1725 0.46 Test anchor Switzerland —Msschler et al (1972) 33 No. 8mm 3 1255 0.69 Test anchor 4 No. 15.2mm 6.5 500 0.47 Commercial anchor Italy —Berardi (1972) 6 No. 15.2rnm 8.4 870 0.36 Commercial anchor 9 No. 13-16mm 3.5 700 0.54 Commercial anchor Germany —Anon (1972)

42 Ground Engineering and Beal (1940) discuss in general terms TABI.E XI—GROUT/STRAND BBOND VALUES WHICH HAVE BEEN EMPLOYED OR the bond characteristics of bars during RECOMMENDED IN PRACTICE pull-out. load As the increases progressive Em- I'h proximal end occurs, and the be-d- Working Test Ultimate location of the maximum intensity o on ment Load bond bond bond Strand tendon (ml (kNl (N/mmtl(N/mmtl(N/mmz Remarks Source stresses moves towards the distal end. The Any type (2.1 Design criteria Australia —Standard CA35 total resistance continues to increase pri- (1973) marily because the length of the tendon Any type 3.105 Design criteria USA —PCI (1974) which has passed its maximum resistance 4 No. 12.7mm 4.3 495 0.72 Test anc h or Switzerland —Sommer et al 1.8 495 1.71 Test anchor (1974) does not release entirely but exerts a resi- 8 No. 12.7mm 5.0 1020 0.64 0.59 Commercial anchor USA—Feld et al (1 74) dual resistance or drag acting concurrent I 8 No. 12.7mm 6.0 1120 y 8 No. 12.7mm 3,6 1350 0.71 with the adhesive bond in the region of 9 No. 12.7mm 5.2 860 0.46 maximum bond stress. Fig. 15 is an ideal- 12 No. 12.7mm 4.5 1410 0.65 12 No. 12.7mm 6.1 1200 0.41 12 No. 12.7mm 5.2 1565 0.63 12 No. 12.7mm 6.1 1335 0.46 Test anchor 12 No. 12.7mm 6.5 1360 0.44 rrl PLAIN BAR 16 No. 12.7mm 6.1 1760 0.45 Commercial anchor Canada —Go)der Brawner lJJ W I- ilJ 54 No. 12.7mm11.3 7010 0.29 z Jz ULTIMATE INTERMEDIATE rll N.B.—In the following, no distinction is made betwe en "Normal" (15.4mm) and "Dyform" (15.2mm) -I o EARLY 1 FIRST SLIP strand. All results sre cele ulated using the smaller dia meter. c) ' 500 Commercial anchor Brita'nin —Universal Anchorage lc \ 4 No. 15.2mm 3.0 0.88 o 'r I IZ U Commmercial anchor USA —Chen et al QO 'I 6 No. 15.2mm 7.3 520 0.25 (197 ) 8 No. 15.2mm 6.1 1500 0.64 Test anchor USA —Nicholson Anchorage ' Co. Ltd. (1973) DRAG 10 No. 15.2mm 6.7 2150 0.67 Commercial anchor Australia' —W')liame 1972 UJ I— 10 No. 15.2mm 6.1 1900 0.65 Commercial anchor Australia —McLeodM et s UJ 12 No. 15.2mm 8 2000 0.44 Commercial anchor Britain —Littlejohn et al ( 13 No. 15.2mm 3 3000 1.61 Test anchor c( 0 ULTIMATE 12 No. 15.2mm 6.5 1950 0.52 Commercial anchor Switzerlandn —Pliskinis 1965) O 18 No. 15.2mm 7.6 4330 0.66 anchor Canada —Go)der Brawner'ommercial

EARLY IN I ERMEDIATE 5 Pn 0 >x/ To 0.2 0.4 0.6 0.6 1.0 =Toe (I (5) 0

where T = bond stress at a distance x from the proximal end (DISTANCE FROM LOADED END OF PULL-OUT SPECIMEN) end 0 = bond stress at the proximal Fig. 15. Quelitetive verietion of (e) bond of the bar stress, (b) total tensile stress, during e 4 = diameter of the bar pull-out test A = a constant relating axial stress in the bar to bond stress in the anchorage material ised diagram showing the progressive nat- ure of bond distribution at successive Assuming the applied tensile load, P, is x/d in- stages ot a test. Curves (a) represent I h sum of the total bond stress tensities of bond stress between the bar multiplied by the surface area of the ten- and concrete. Curves (b) maya bee con- don, Phillips (1970) extended the above .01 sidered as stresses in bar, at successive theory as follows: 10 I n the specimen. It should be .41 e 'ITd recognised that for curves ( ), L T0 point (rate — tensity of bond stress at any P = 0j crdr,.dx= (1 e ) A 12 sented by the slope of the curve, with " """"".(6) the axis of the specimen, at Fig. 16. Theoreticei stress distribution between the limits x = o an x = L, where tthat8 ppoint.'. Bondon is what makes stress along an anchor The transfer possible and can be present only L isteh I engn th of the fixed anchor. (after Hawkes sr Evans, 1951) in the steel lengt h of th e anchor will depend upon thee in a region of changing stress 2 or the concrete. axial distance required to transfer the oa ITx/pl il d (transmission length Considering Fig. 15, it is apparent that across the interface 0 02 0.4 06 0.6 10 for a plain bar pull-out test: Bond resistance is first developed near At x = L,, T, approaches 0 and from (5) (i) in- the proximal end of the bar, and only as it can be seen that Ax/d approaches ' slig t I'curso are tensions and bond finity, giving sip de stresses tranansmitted progressively dista II y. Jr T0 P = (ii) The region of maximum intensityit oof A " (7) bon d stress moves away from the proximal end as the pull increases. Between the Substituting equation (5) into equation pro ima I enden aand the region of maximum gives bond stress there is a fairly uniform (7) tional or drag resistance of greatly reduced ez —(crds) = Ae d x/d P ("') I f r the (III) "First slip" occurs only a ter t e (8) maximum intensity of bond resistance has "" speci- travelled nearly the full length of the Equations (5) and (8) are represented 10- men and has approached the distal end of grap h'lica y in Figs. 16 and 17 which show the bar. the variation of shear stress a ong Fig. 17. Load distribution along en (' Aft r appreciable slip, the primary anchorage and its dependence upon the anchorage assuming AL/d is large adhesive resistance disappears and the constant A. The greater the value of A, the (after Phillips, 1970) offers a frictional or drag resistance h tress concentration at the free throughout its entire length, amounting to or proximal end of the anchor. The smaallerer sent on th e behaviour of cement grout perhaps half the ultimate total resistance the value of A the more evenly the stresses anchors in rock to provide meaningfu ul attained. are distributed along the length of anchor. values for A. It is reassuring however, to In Britain, Hawkes and Evans (1951) Although values for A have been ob- find that the results in Fig. 17 are very were able to conclude from pull-out tests taine'd foro steel anchorages embedded in similar to the results of Coates and Yu that the distribution of bond obeys an ex- concrete —Hawkes and Evansns giveive A= (1970) in Fig. 8 with E„/E„proportional to ponential law of the form: 0.28—insufficient information exists at pre- 1/A, which suggests that the basic ap- July, 1975 43 proach of Hawkes and Evans is applicable three months exposure, developed greater FIP (1974) also confirms that strand tends to rock anchors. bond than unrusted or wiped rusted bars. to be more popular than wire, and the use (iii) The loose powdery rust which ap- of strand is now accepted even in coun- pears on bars during the first few weeks of tries where the basic material cost is Magnitude of bond ordinary exposure has no significant effect greater. It is now widely recognised that Bars. In a rigorous investigation of the on the bond of bars. the smaller the diameter of the tendon, the bond between concrete and steel bars, properties These findings have also been confirmed less is the cost of the material unit of Gilkey, Chamberlin and Beal (1940) em- per Kemp et al for deformed force, but direct compari- phasise the following major poihts relevant by (1968) bar, prestress cost and to rock anchors: Armstrong (1948), Base (1961) and sons for the supply of tendon material in Hanson for wire and strand. since 1. Contrary to accepted belief, bond re- (1969) any country can be misleading the real of the tendon also sistance is not proportional to the com- cost reflects cost of fabrication, pressive strength of a standard cured con- Remarks installation and stressing. Some designers consider the question of crete, there being some increases in bond grout/tendon bond in anchor systems to but a reduction in the ratio of bond resis- Tendon characteristics present no the With characteristics it tance to the ultimate compressive strength problems, as design at the regard to general rock/grout interface is more critical. There- is of value know in Britain the as the strength of concrete increases, to that pro- fore any embedment length accommodat- duction of prestressing tendons is gov- especially for the higher strengths. To be ing that interface automatically erned 4486:1969 specific, for the weaker concretes (UCS ensures a by BS (Cold Worked high factor of High Tensile 21N/mms) bond increases with the safety at the tendon/grout Alloy Steel Bar), BS 2691: ( interface. A factor of compressive strength. However, as the of safety at least two 1969 (Steel Wire), BS 3617:1971 (7 Wire is allowed other and BS Wire concrete strength exceeds this value, the by designers. Strand) 4757:1971 (19 While there is an appreciable amount of Strand) increase in bond resistance becomes less, . information available concerning the mech- Following publication of CP 110:1972, and within the strong concrete range i.e. anism of bond transfer in field of rein- permissible are in terms of UCS 42N/mm', no added bond allow- the stresses quoted ) forced and prestressed it is con- the specified characteristic strength which ance is justified for added strength of con- concrete, crete. sidered that much more study is required is the guaranteed limit below which not in the field of rock anchors. The mode of more than 5 per cent test results fall, and 2. The bond developed by added length failure of a tendon bonded into the none of these is less than 95 cent of embedment is not proportional to the grout per of an in situ rock anchor dissimilar strength. For wire and additional length. The shorter the embed- may be characteristic to that of the tendon pull-out in the specified minimum is ment, the greater is the average unit bond test used strand, strength concrete technology and from which most taken as the characteristic strength, which stress that can be developed by a plain data are obtained. In bar. Therefore doubling the length of em- the former case the for practical purposes is termed 100 per grout is usually in tension, bedment as a means of increasing the whereas during cent fpu. a standard bond anchorage does not actually double the test, part, at least, of the At home and abroad it is common to find surrounding in in such amount of tension that the bar can resist concrete is compression. tendon stresses quoted terms as In rock anchors, therefore, the mechanism elastic limit, 0.1 per cent proof stress and by bond. On the other hand, additional of bond action on the Therefore embedment does add to the sum total of depends respective 0.2 per cent proof stress. to elastic moduli of the bond resistance. steel and grout. facilitate understanding and comparisons, Little work has been done on multi-unit some reconciliation is required between 3. Variations in age and type of curing tendons with In seem to alter bond resistance much less respect to their bond distri- these terms and characteristic strength. bution. The use of spacers and centralisers, this connection it is noteworthy that in the than they alter the compressive strength leading possibly to decoupling, also war- preamble to the French Code (Bureau of the concrete, bearing in mind that the rants investigation. strongest concrete gives the higher bond, Securitas 1972) the term Tg is identified In general, but the weakest concretes have the highest recommendations pertaining and defined as the elastic limit, measured to grout/tendon bond cur- ratio of bond to compressive strength. values used as the 0.1 per cent proof stress, i.e. that rently in for rock com- Little information is available on the practice anchors point at which the permanent elongation monly take no of effect of spacing but Chamberlin (1953) account the length and reaches this value. The same note draws of tendon, tendon conducted a series of tests with various type geometry, or grout attention to the fact that this limit should strength, and for these reasons it is still not be confused with the types of bars to determine the effect of 0.2 per cent proof advisable to measure in the British spacing on bond magnitude. For clear spac- experimentally the stress adopted Codes. Based embedment length for known field condi- on wire metallurgists of 1d and 3d differences in bond were the advice of the ings tions. not significant. authors understand that the 0.1 per cent Wires and strand. Based on results ob- proof stress varies from 3-5 per cent below tained from almost 500 pull-out tests, TENDON the 0.2 per cent proof stress which is de- Stocker and Sozen (1964) conclude: Introduction fined as 87 per cent fpu in CP 110. Taking Accurate data Due to the helical arrangement of the on the mechanical prop- the average figure of 4'er cent below 0.2 (a) erties exterior wires, strand rotates while slip- of tendon components are readily per cent proof stress, then a 0.1 per cent available, but the choice of of ten- proof stress is equivalent cent ping through a grout channel, but the in- type to 83.5 per don and safety factors to be This correlation crease in bond is not significant. (Ander- employed fpu. may be employed son et al (1964) also observed rotation of against rupture still demand assessment when comparing safety factors in subse- and the strand of about 15 deg during pull-out judgement by designer, especially quent tables. tests.) in countries not covered by a code rela- With respect to the values of elastic ting to anchors. modulus Bond magnitude increases by ap- quoted subsequently, it is known (b) Tendons be formed al- proximately 10 per cent per 6.9N/mm'f may of bar, wire or that an error of 5 per cent is possible, strand. The latter two have advan- within concrete compressive strength, in the distinct though the majority of results are 16.6-52.4N/mm'. tages with respect to tensile strength, ease three standard deviations from the mean. range of Results from pull-out tests subjected storage, transportation and fabrication. Knowledge of this possible variation can (c) Bars, however, are more to externally applied lateral pressures rang- readily protected be very important when interpreting load- from 0-17.25kN/ms indicate a linear in- against corrosion and in the case of shal- extension graphs and for the same reason ing low, low anchors, crease of bond strength with lateral pres- capacity are often easier relaxation characteristics of tendons should and cheaper to install. de- sure. In connection with this, concrete be assessed carefully. Both aspects are Largely as a result of in shrinkage is clearly important. recent develop- tailed Part 3 of this review, but it is of ments in prestressing equipment and tech- general interest to know that relaxation niques, the use of strand appears to be in- loss is a function of the logarithm of time. Effect of rust on bond creasing in popularity. A recent survey by For example, the loss after one hour is Gilkey et al (1940) also investigated the bond- effect of steel surface conditions on TABLE XII—TECHNICAL DETAILS OF BRITISH PRESTRESSING BARS ing properties and found that: (i) Deep flakey rust on bars, following Bar diameter (mm) item Uni t Rem sr ks 6-8 months exposure, lowers the bond, but 20'2 25'8 32'5 40e 4x32 4x40 wiping the loosest rust off finally produces Sectional area mmt 314.2 380.1 490.9 615.8 804.3 962.1 1256.6 3217 5026 In each case, the a surface that will develop a bond equal to ciraracteristic or greater than that which the bar would Minimum k N 325 375 500 625 1250 3200 5000 tensile strength is breaking load 1000N/mmt have developed in the unrusted condition. (ii) Slightly rusted bars, following up to 'Recommended sizes 44 Ground Engineering 50-60 per cent of that at 100 hours, which u) 0 I in turn is about 80 per cent of that at 1000 STABILIZED WIRES AND STRANDS hours. The loss at 1000 hours is also about half that at 5-8 years. Relaxation loss de- pends on the initial stress in the tendon and production history, and whilst tendons of RANGE OF VALUES FOR STRESS RELIEVED WIRES exceptionally low relaxation properties can tL be produced, the anchor designer should re- ALLOY STEEL BARS' member that little advantage will be gained o< their if for creep in through use, example z RANGE OF VALUES the ground is likely to be large in compari- "~~ STRESS RELIEVED STRANDS son. f. Bars. CP 110 (1972) quotes detail sup. RANGE OF VALUES FOR 19 WIRE STRANDS ( NOT S(R ) plied by McCalls Macalloy Ltd. (1969) on typical British bars in use (Table XII). The 6. modulus of elasticity is about 165 000 N/mrna, although CP 110 suggests a value ui 9,- of 175 OOON/mm'. ui With regard to relaxation Antill (1965) 10 100 SOO found that the load loss for a typical alloy 010 steel bar, initially stressed to 70 per cent TIME AFTER STRESSING —HOURS UTS is about 4 per cent at 1 000 hours, and double that at 100000 hours. For compari- Fig. 18. Relaxation of British tendons at 20'C from initial stresses of 0.7 UTS son the performance of bars relative to other tendon components is shown in Fig. 18. This information is provided for de- 20 No. 20mm plain bars for a 1 750kN test of capacity 1 375-1 865N/mm'o meet the signers bearing in mind that CP 110 ad- anchor. Soviet Code GOST, 7348-63. A popular vises that an "appropriate allowance for 2. Wires. Prestressing wire is manufac- choice for anchors is 5mm wire (1670 relaxation" be made "for sustained loading tured from cold drawn plain carbon steel, N/mm'), with elastic modulus 184000 conditions". and in a few countries, for example Ger- N/mm'nd 6.8 per cent relaxation at 1 000 The use of bar anchors is very popular in many, quenched and tempered (oil hard- hours. Wire tendons are recommended by Germany and North America, where bar ened and tempered or oil hardened) varie- Shchetinin on the basis that they eliminate sizes are available from 6.4mm (No. 2 bar) ties predominate. suspected torsional and bending problems to 25.4mm (No. 8 bar) in steps of 3.2mm, The ultimate tensile strength is inversely of strand anchors. and thereafter to 35.8mm (No. 11 bar) in proportional to wire diameter, but also de- In general, tendons comprise between 10 slightly larger increments. pends on the method of manufacture, and and 100 wires (5-8mm diameter), depend- Bars tend to be used as tendons in fairly the steel specifications of the country con- ent on the required anchor capacity, but short low-medium capacity anchors mainly cerned. 660 No. 5mm wires were employed at the in single bar situations, but are increasingly The major properties of British wire are Cheurfas Dam by Soletanche in 1934. used in certain sophisticated forms in Ger- summarised in Table XIII. CP 110 indicates 3. Strand. All strand is made from cold many, where compression tubes and elabor- that a typical value for the elastic modulus drawn plain carbon steel wire in Britain ate end bearing devices are incorporated. of wire and small diameter strands is and seven wire strand is by far the most Groups of up to four bars have been used 200 OOON/mm'. popular. Seven wire strands are stress re- on occasions, but larger groups are rare It is noteworthy that Shchetinin (1974) lieved after stranding to produce 8 "normal although Berardi (1960) successfully used reveals that Soviet industry produces wires relaxation" type, in two grades —regular

TABLE XIII—TECHNICAL DETAILS OF BRITISH TABLE XIV—TECHNICAL DETAILS OF BRITISH PRESTRESSING PRESTRESSING WIRE STRAND

Wiie diameter Characteristic Average strength (N/mmt) Remarks relaxation (mmi at 1000 hrs Mill coil (BS 2691 Sect. 4i from 70 Minimum per cant 1570e E(N/mm') = 192 000 breaking ultimata at 1670 0.2 par cant stress = 75 par cant specified Dia load Average E. 20 dag C 1720 minimum strength. (mmi (kN) (N/mmti (per cent) Remarks 1620e Average relaxation at 1 000 hours from 1570e cant = 8 par cant ultimata at 5.0'.5'.0'.25'.0 70 par Regular.: normal relaxation (BS 3617 Sect. 2) 1670 20 dog C 1770 44.5 198000 5.6 The load at 1.0 par cant extension or 1670 7.9 69.0 198 000 (7 0.2 par cant proof load = 89 ar cant 1720 9.3 93.5 198 000 maximum) actual breaking load (average%. 1770 10.9 125.0 198 000 The load at 0.01 par cant proportional 1670 12.5e 165.0 198 000 limit = 73 par cant actual breaking 1720e load. (average) 1770 Regular. Iow relaxation (BS 3617 Sect. 3) 2.65 1770 4.0'verage 000 1.1 The load at 1.0 par cant extension —— 1870 9,3 93.5 200 2.0 2020 10.9 125.0 200 000 (2.5 89 par cant actual breaking load 12.5e 165.0 200 000 maximum) (average). Praatraightan ad —Normal relaxation BS 2691, Sect. 2) 15.2e 227.0227,0 200 000 The load at 0.01 par cant proportional ( limit = 80.5 par cant actual breaking 8.0 1470 Average E(N/mmt) = 201 000 load (avaraga) 1570 1470 0.2 par cant proof stress = 85 par cant Super. normal relaxation 7.0'.0 1570 specified minimum strength. 9.6 102.5 197 000 5.5 Load at 1.0 par cant extension = 85 1670 11.3 138.0 197 000 (7 par cant actual breaking load 1470 Average relaxation at 1 000 hours from 12.9'84.0 197 000 maximum) (average). 70 par cant = 3.8 par cant ultimata at 1570'670 15.4'50.0 197 000 Load at 0.01 par cant proportional 20 dag C limit = 76 par cent actual breaking 5.0e 1570'670 load (avaraga) 1720 Super. Iow relaxation 4.5 1570e 9,6 102.5 198 000 1.15 Load at 1.0 par cant extension = 1670 11.3 138.0 198 000 (2.5 90 par cant actual breaking load 172n 12.9e 184.0 198 000 maximum) (average) . sizes 1570'670 'Preferred 15 4e 250.0 198 000 Load at 0.01 par cent proportional limit = 79 par cant actual breaking 1770 load (average) Dyform 12.7» 209.0 198 500 Load at tio par cant extension = 15.2'00.0 196 500 92 par cant, 92 par cant and 91 par 18.0'80.0 195 100 cant actual breaking load, respectively (average) Load at 0.01 par cant proportional limit = 85 par cant, 85 par cant and 83 par cant actual breaking load, respectively (avaraga) 'Preferred sizes July, 1975 45 and super. "Low relaxation" strand is pro- TABLE XV—ALLOWABLE STRESSES AND SAFETY FACTORS WHICH HAVE BEEN duced by a patented stabilisation process RECOMMENDED FOR ANCHOR TENDONS of applying a tensile stress to the strand during the stress relieving process. Again Working Test Mea- stress stress sured Ultimate two grades are available. In addition, strand (per (per safety safety may be subjected to a compacting, or "dy- cent j cent) factor factor Remarks Source forming" process whereby about 20 per 50 75 1.5 2 With respect to (w.r.t.) Britain —Littlejohn (1973) cent more of the nominal cross-sectional characteristic tensile strength area is occupied by steel, with respect to (50 70 1 5 )2 w.r.t. Britain —Mitchell (1974) characteristic tensile ordinary strand, and so higher loads can be strength 50 75-80 1.5-1.6 2 w r.t. Britain —Ground Anchors Ltd. (1974) sustained. Such strand also has low relaxa- 80 characteristic tensile strength Britain —CP 110 (1972) tion properties. w.r.t. yield strength DIN The mechanical properties of British (60 (90 1.5 1.75 Germany — 4125 (1972) seven wire strand are summarised in Table 70 77 1.1 1.43 "Swissboring SA" BBRV Switzerland —Descoeudres (1969) anchors XIV, bearing in mind that the values of mini- (69 (90 )1,3 )1,45 w.r.t. yield strength Switzerland —Draft recommendations mum breaking load and elastic modulus (1973) may vary by up to 8 per cent and 5 per cent (70 (95 1,43 w.r.t. Oi1 per cent residual France —Fargeot (1972) respectively. elongation Nineteen wire strand is available in dia- 60 w.r.t, the elastic limit France —Adam (1972) meters of 22.2, 25.4, 28.6, and 31.8mm, with 53-66 80 1.2-1.5 1.5-1.9 w.r.t. ultimate tensile strength France —Fenoux et al (1972) minimum breaking loads of 503.1, 658.9, (60 1.3 2 w.r.t. elastic limit France —Bureau Securitas (1972) 823.6 and 1 002.0kN respectively. 1 5-2 w.r.t. elastic limit ln general, tendons comprise between Italy —Mascardi (1972) four and 20 strands (12.7 and 15.2mm dia- 65 or 1 54 w.r.t. ultimate tensile strength Finland —Laurikainen (1972) meter) but 54 No. 12.7mm strands were 85 w.r.t. elastic limit Finland —Laurikainen (1972) used for 7010kN in capacity anchors the 59 or 1.69 w.r.t. ultimate tensile strength Czech os love k ia—Voves (1972) Interstate 1-96 Highway retaining wall, 71 w.r.t, elastic limit Czechoslovakia —Voves (1972) Detroit, USA. (57 (69 )1.2 )1.75 w.r.t. ultimate tensile strength Czechoslovakia —Draft Standard (1974) Allowable stresses and safety factors 60 80 1 33 1.67 w.r.t. ultimate tensile strength Canada —Golder Brawner Assocs. In Britain, the vast majority of anchor ten- (1973) dons with are designed a working stress of 50 75 2 1.5 w.r.t. ultimate tensile strength USA —vVhite (1973) 62.5 per cent fpu i.e. a factor of safety 55-60 1.7-1.9 w.r.t, ultimate tensile strength Brazil —da Costa Nunes against failure of 1.6. However, in recent (1971) w.r.t. elastic ilimit Brazil —da Costa years several publications have suggested 90 Nunes (1971) that whilst this approach is acceptable for 65 or 1.1 1.54 w.r.t. ultimate tensile strength South Africa —Parry-Davies (1968) temporary anchors (working life less than 80 w.r.t. yield strength South Africa —Parry-Davies (1968) two years), the design stress for permanent (70 )1.2 1.43 w.r.t. ultimate tensile strength South Africa —Johannesburgh (1968) tendons should be reduced to 50 per cent (70 )1.43 Wires w.r.t. ultimate tensile South Africa —Cods (1972) ) strength fpu, giving a safety factor of 2 and permit- (67 1.49 Bars w.r.t. ultimate tensile South Africa —Code (1972) ting a larger test overload. Since the French ) strength Code is widely OI'0 (1972) recognised as one 1 25 )1.49 Bars w.r.t. 0.2 per cent proof South Africa —Code (1972) of the most authoritative documents on strength ground anchors published to date, it is en- 75 w.r.t. ultimate tensile strength Australia —Koch (1972) couraging to observe that for temporary (60 )1.67 w.r.t. ultimate tensile strength Australia —Code CA 35 (1973) and permanent anchors, the Bureau Securi- 9) 80 1 6 2 w.r.t. ultimate tensile strength New Zealand —Irwin (1972) tas recommend design forces of 0.75Tg and 0.6Tg, respectively. As shown earlier, Test load Measured safety factor = / Tg is the elastic limit which is equivalent to Working load 83.5 per cent fpu and thus it may be calcu- Failure load Ultimate safety factor = / lated that the French recommendations are Working load almost identical to those presented in re- cent British publications. To provide a more general picture, Table TABLE XVI—DESIGN STRESSES AND SAFETY FACTORS WHICH HAVE BEEN XV shows recommendations made in Codes EMPLOYED IN PRACTICE FOR BAR TENDONS of Practice, and by practising engineers, throughout the world. For convenience, Working stress Test stress Measured Ultimate only permanent anchors have been con- (per cent (per cent safety safety sidered. Bar ultimate j ultimate j lector factor Source It would appear that there is a definite trend towards raising both the measured 28mm Lee Macalloy 70 1.43 Britain —Banks (1955) and ultimate safety factors, to 1.5 and 2.0 32mm Mace lloy 56 84 1.5 1.79 Britain —Jackson (1970) respectively; this is undoubtedly an en- 32mm hollow 54 64 1.2 1.85 Sweden —Nordin (1968) couraging feature, at a time when larger 35mm 50 75 1.5 2 USA —Drossel (1970) capacity anchors are being installed, often 22mm HS 47 52 1.1 2.1 USA —Koziakin (1970) in poor quality rock. In such conditions a HS bars 1.5 USA—Wosser et al (1970) large test overload is considered necessary 35mm Bauer 44 1.2 2.27 USA —Larson et al (1972) for security, and this can be achieved 27mm Dywidag 55 1.06 1.82 Japan —Construction Ministry only (1964) by a reduction in the level of working stress to about 50 per cent ultimate. Otherwise, permanent set may be induced in the ten- don. TABLE XVII—DESIGN STRESSES AND SAFETY FACTORS WHICH HAVE BEEN EMPLOYED IN PRACTICE FOR WIRE TENDONS Tables XVI-XVIII have been prepared from provided in data papers describing this Work stress Test stress Measured Ultimate aspect of anchor design. A number of ex- (per cent (per cent safety Safety amples are quoted for each type of tendon Wi re ultimate j ultimate j factor factor Source for purposes of illustration and discussion. Smm 64 74 1.36 1.57 Britain —Morris et al (1956) The average working stress is highest for 7mm 63 69 1.1 1.59 Britain —Gosschalk et al (1970) wires and lowest for bars; the safety factor 7mm 66 79 1.2 1.52 Switzerland —VSL (1966) against rupture of the tendon is thus in the 8mm 68 82 1.2 1.47 Switzerland —VSL (1966) inverse relation. Testing to 1.5 times the 8mm 50 65 1.3 2.0 Switzerland —Moschler et al (1972) working stress seems at present to be the 6.4mm 60 1.08 1.67 Canada —Golder Brawner Assocs. (1973) exception rather than the rule, and com- 6.4mm 60 73 1.17 1.67 USA —Eberhardt et al (1965) monly contract anchors are over-pre- 7mm 60 62 1.03 1.67 Australia —Rawlings (1968) stressed by an amount thought equivalent 46 Ground'ngineering TABLE XVIII—DESIGN STRESSES AND SAFETY FACTORS WHICH HAVE BEEN anchor heads will be discussed in Part 3 of EMPLOYED IN PRACTICE FOR STRAND TENDONS this review. Working stress Test stress Measured U(time te General conclusions . (per cent (per cent safety safety Although rock anchors have been used- Srrand ultimate) u(timete factor factor Source ) for over 40 years, it is difficult to justify 15.2mm 55 61 1.1 1.82 Britain —Ground Anchors Ltd. (1973) technically certain aspects of contemporary 15.2mm 58 80 1.37 1.71 France —Soletanche (1968) 12.7mm 48 57 1.2 2.1 Switzerland —VSL (1966) design. Progress in the development and 12.7mm 30 73 2.43 3.3 Switzerland —Summer et al (1974) rationalisation of design has been slow, 12.7mm si 60 1.67 Canada —Golder Brawner (1973) 15.2mm largely due to the scarcity of reliable lab- 12.7mm 65 80 1.23 1.54 Canada —Golder Brawner (1973) oratory and field experimental data relating 15.2mm 50 80 1.6 2.0 Canada —Golder Brswner (1973) 12.7mm 52 78 1.5 1.93 USA—White (1963) directly to rock anchors. 12.7mm 60 80 1.33 1.67 USA—Buro (1972) As a result, practising engineers have 15.2mm 59 79 1.34 1.69 USA—Schousboe (1974) 12.7mm 60 85 1.42 1.67 Australia —Langworth (1971) been obliged to make reference to values and methods employed with apparent suc- cess in earlier designs, without fully appre- TABLE XIX—PITCH OF TENDON SPACERS IN THE GROUTED FIXED ANCHOR ZONE ciating or understanding their accuracy or reliability. Bearing-this in mind, it is perhaps Pitch of tendon understandable that the majority of designs spacers are overconservative in certain aspects, if (m) Remarks Source not in all. This dilemma is becoming increas- 0.5 Cheurfas Dam USA—Zienkiewicz et al (1961) re- 0.5 3m fixed anchor Czechoslovakia —Hobst (1965) ingly acute now that engineers are being 0.8 Multi-wire tendons France —Cambefort (1966) quested to design for circumstances where 0.6 VSL anchors Switzerland —Losinger SA (1966) no exist. 0.8-1.6 Multi strand tendons Britain —Littlejohn (1972) exact precedents 2.0 Multi strand tendons Italy —Mascardi (1972) In view of the inconsistencies between 0.5-2.0 Dependent on "stiffness" Germany —Stocker (1973) high- of tendon system theory and practice which have been 1.5-2.0 Conenco (Freyssinet) Canada —Golder Brawner Assocs. (1973) lighted in this design review, it is con- anchors sidered that more attention should dir- 1.8 7.3m fixed anchor USA —Chen et al (1974) be 2.0 Sm fixed anchor Britain —Littlejohn et al (1974) ected towards studies in the following (12 No. 15.2mm strands) 0.5 Multi-wire tendons USSR—Shchetinin (1974) areas: f. Uplift capacity. There is little justifica- tion for the inverted cone method of assess- to long term load losses —usually 10 per lock between the tendon and surrounding ing the ultimate resistance of withdrawal of cent. grout. Whilst this method gives a tendon the rock anchor system. However, until full- geometry which allows adequate penetra- scale field tests are carried out to study Tendon spacers tion and cover of grout, it is important to modes of failure in relation to the geotech- Spacers are used in both the free and note that the practice of unravelling strands nical properties of rock masses, the present fixed sections of multicomponent tendons. followed by bushing of the wires gives a method of design, where rock shear In the free length they may serve to centra- random geometry which cannot guarantee strength is ignored, must be persevered lise the tendon with respect to the borehole efficient load transfer. with, as it is basically very conservative. but their main function is to prevent tang- With reference to the pitch of spacers, Nevertheless, some standardisation on ac- ling or rubbing of the individual bars, wires Table XIX gives an indication of the dis- ceptable modes of failure, safety factors or strands. This is particularly important in tances which have been employed in prac- and allowances for unconsolidated over- long, Rexible tendons, where, if the ten- tice. In general it would appear that little burden is now required. don is allowed to lose its design geometry, work has been carried out on the influence 2. Fixed anchor. A uniform distribution of load may be dissipated through friction in of pitch or spacer design on load transfer bond stress is assumed in the vast majority the free length during stressing. In addition, in the fixed anchor zone. of anchor designs, although this approach is extremely high stress concentrations may only valid in the case of soft rock. In hard develop, particularly just under the top Remarks rock, the stress distribution is non-uniform, anchor head, where rupture of individual Whilst tendons are produced to a high the highest stresses being mobilised at the elements can easily occur. Spacers in this standard and reliable minimum breaking proximal end of the grouted fixed anchor part of the anchor are hollow cored and loads are specified for use by the designer, zone. The ratio Ex„,„,/E„„khas a major in- between 4-Sm apart. few load/extension tests have been carried fluence on stress distribution, although the In the grouted fixed anchor zone the out on long tendons (10-30m) which are authors find that rock masses are seldom spacers encourage effective penetration of comparable in size to the free anchor classified in sufficient detail for other poten- grout between the tendon units, thereby lengths used in practice. Since interpreta- tially important parameters to be high- ensuring efficient transmission of bond tion of anchor load/displacement character- lighted. The phenomena of debonding in stress. In addition the spacer units should istics can be quite controversial in prac- rock anchors is not well understood, al- be designed to centralise the tendon in the tice, particularly in the case of strand, it though it has undoubtedly been significant borehole to (a) avoid contamination of would be of value to know if long strand in certain high capacity anchors described. tendon e.g. clay smear, and (b) give ade- tests give E values which are significantly Values for the magnitude of bond at the quate cover of grout for corrosion protec- different from those obtained using short grout tendon interface are usually abstrac- tion and good grout bond at the borehole gauge lengths of 0.61m. The influence of ted from publications relating to reinforced interface. tendon curvature, and splaying of multi- and prestressed concrete. However, it Spacers in this zone may also be used component tendons near the top anchor should be noted that the boundary condi- in conjunction with intermediate fasten- head on stress/strain behaviour also re- tions existing in conventional bond tests, ings to form nodes or waves, in order to quires clarification in view of the dearth of may be wholly different from these present provide a more positive mechanical inter- published information, at present. Top in the rock anchor situation.

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