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Journal of Rock Mechanics and Geotechnical Engineering 7 (2015) 1e13

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Journal of Rock Mechanics andGeotechnical Engineering

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Review

Rock engineering design of post-tensioned anchors fordams e A review

E.T. Brown*

Golder Associates Pty Ltd., PO Box 1734, Milton, Queensland 4064, Australia

a r t i c l e i n f o

Article history:Received 15 August 2014Accepted 18 August 2014Available online 18 September 2014

Keywords:Dam engineeringPost-tensioned anchorsRock engineering designGroutetendon bondRockegrout bondRock mass uplift failure

* Tel.: þ61 7 3721 5451.E-mail addresses: tbrown@golder.com.au, et_browPeer review under responsibility of Institute o

Chinese Academy of Sciences.1674-7755 � 2015 Institute of Rock and Soil Mechanences. Production and hosting by Elsevier B.V. All righttp://dx.doi.org/10.1016/j.jrmge.2014.08.001

a b s t r a c t

High-capacity, post-tensioned anchors have found wide-spread use, originally in initial dam design andconstruction, and more recently in the strengthening and rehabilitation of concrete dams to meetmodern design and safety standards. Despite the advances that have been made in rock mechanics androck engineering during the last 80 years in which post-tensioned anchors have been used in dam en-gineering, some aspects of the rock engineering design of high-capacity rock anchors for dams havechanged relatively little over the last 30 or 40 years. This applies, in particular, to the calculations usuallycarried out to establish the grouted embedment lengths required for deep, post-tensioned anchors.These calculations usually make simplified assumptions about the distribution and values of rockegroutinterface shear strengths, the shape of the volume of rock likely to be involved in uplift failure under theinfluence of a system of post-tensioned anchors, and the mechanism of that failure. The resulting designsare generally conservative. It is concluded that these aspects of the rock engineering design of large, post-tensioned rock anchors for dams can be significantly improved by making greater use of modern,comprehensive, numerical analyses in conjunction with three-dimensional (3D) models of the rock massstructure, realistic rock and rock mass properties, and the results of prototype anchor tests in the rockmass concerned.� 2015 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by

Elsevier B.V. All rights reserved.

1. Introduction

Ground or rock anchors (sometimes referred to as anchorages) ofa number of types have long been used for a range of purposes inrock engineering and in geotechnical engineering more generally(Hobst and Zajíc, 1977; Hanna, 1982; Habib, 1989; Xanthakos, 1991;Littlejohn, 1993, 1997). Rock anchors are capable of transmitting anapplied tensile load to the rock mass and may be used, for example,to reinforce rock slopes and underground excavations; stabilisesheet pile, diaphragm and retaining walls; anchor building, bridge,power transmission line and other tower or mast structure foun-dations; anchor marine structures; stabilise large excavations suchas dry or graving docks potentially subject to uplift; and for anumber of purposes in damengineering to be discussed in Section 2.

Depending on their purpose, rock anchors may be temporary orpermanent, and may be passive or post-tensioned (sometimesreferred to as pre-stressed). They may also vary greatly in

n@bigpond.com.f Rock and Soil Mechanics,

ics, Chinese Academy of Sci-hts reserved.

orientationwith respect to vertical, in size (including in both lengthand diameter), in the nature and size of the tendon (bar, wire orstrand, either singly or in groups) providing the essential tensilecapacity, and in the ultimate load-carrying capacity of the anchor.In this paper, emphasis will be placed on large-scale, high-capacity,permanent rock anchors of the type illustrated schematically inFig. 1. Features of this class of rock anchor include the provision of afixed anchor or tendon bond length, a free tendon length, astressable (and preferably re-stressable) anchor head, and doublecorrosion protection. Obviously, in terms of their scale, purposes,rock engineering design and detailed design and installation, theselarge rock anchors can differ significantly from the rock bolts, cablebolts and rock socketed piles used widely in surface and under-ground construction and mining. However, these elements all havesome features in common that allow data, understandings and el-ements of design approaches to be transferred from one applicationto another.

The purpose of this paper is to review international practice inthe rock mechanics and rock engineering design of rock anchorswhich, as will be shown, has remained largely unchanged since the1970s. The paper will deal mainly, but not exclusively, with thedesign of large anchors of the type shown in Fig. 1 and with theirapplication in dam engineering, particularly for concrete gravity,buttress and arch dams. Some emphasis will be placed on Austra-lian practicewhich is the source of the author’s practical experience

Stressing jackAnchor headBearing plate

Tendon

Drilled hole

Cement grout

Smooth p.c.sheath

Corrugatedp.c. sheath

Bon

dle

ngth

Free

leng

th u

nbon

ded

Stre

ssin

g le

ngth

Ove

rdr

ill

Free

len

gth

Bon

dle

ngth

Fig. 1. Components of a typical large, permanent, post-tensioned dam rock anchor(Cavill, 1997).

E.T. Brown / Journal of Rock Mechanics and Geotechnical Engineering 7 (2015) 1e132

in this area. It is recognised that some of the terminology used maydiffer from country to country.

2. Post-tensioned anchors in dam engineering

Post-tensioned, and in some cases, passive (Hobst and Zajíc,1977; Bretas et al., 2010) rock anchors have been used for a rangeof applications in dam engineering over the last 80 years (Bruce,1988). These applications include providing:

� resistance to overturning (Banks, 1957; Khaoua et al., 1969);� restraint against downstream sliding (Maddox et al., 1967;Gosschalk and Taylor, 1970);

� reinforcement of excavated abutment and other slopes (Liang,1995; She, 2004);

� stabilisation of thrust blocks (Dickson and Loar, 2011);� additional seismic resistance (Singhal and Nuss, 1991; Bianchiand Bruce, 1993; Lawrence and Martin, 2007);

� tying down of spillway, training wall and stilling basin struc-tures (Hobst and Zajíc, 1977; Cavill, 1997; Topham et al., 2013);

� stabilisation of plunge pools and other erosion features (Loweet al., 1979; La Villa and Golser, 1982); and

� raising and/or strengthening older dams that no longer meetsafety or capacity requirements (ANCOLD, 1992; Xu andBenmokrane, 1996; Cavill, 1997; Snape, 2002).

The first recognised use of post-tensioned anchors in dam en-gineering was for the raising and strengthening of the 30 m highCherfas gravity dam in Algeria in 1936 (Hobst and Zajíc, 1977;Khaoua et al., 1969). For some time following their introductioninto dam engineering, post-tensioned anchors were used in theinitial design and construction of concrete dams and their appur-tenant structures (e.g. Banks, 1957; Wilkins and Fidler, 1959;Maddox et al., 1967; Gosschalk and Taylor, 1970; Hobst and Zajíc,1977). More recently, the major use of post-tensioned anchors indam engineering has been for the raising or strengthening ofexisting dams.

Xu and Benmokrane (1996) carried out a major review of thethen state-of-the-art of the strengthening of existing concrete

dams using post-tensioned anchors. They listed the main reasonsfor strengthening existing dams as being to:

� meet changes in safety standards;� overcome deficiencies in design and construction;� recover loss of strength due to deterioration; and� raise the heights of dams.

In many countries, the former dam safety standards and designcriteria based on historical flood levels have been replaced bycriteria based on probable maximum flood (PMF) or probablemaximum precipitation design flood (PMP DF) water flows andlevels. The predicted design flood levels based on annual exceed-ance probabilities (AEPs) can be higher than the historical levelsused in the original designs, so that the design spillway capacities ofmany existing dams are inadequate to pass the new design floodssafely. Furthermore, the dams may potentially fail by overturningand/or sliding. This is particularly the case for dams designedbefore about 1946 (in Australia, and at other times elsewhere)when uplift forces acting on the base of the dam were not allowedfor adequately in design calculations (ANCOLD, 1992; Cavill, 1997;Kline et al., 2007; Duffaut, 2013). As a result, many existing damshave been in need of upgrading, including raising, to meet the newdesign flood and related stability criteria. Another change in safetystandards has been the application of maximum credible or designearthquake (MCE or MDE) criteria (Xu and Benmokrane, 1996;Bruce, 1997). Detailed discussion of these issues is beyond thescope of this paper. However, it is important to note that safetystandards and terminologies may differ between countries andjurisdictions. For example, in the author’s home State of Queens-land, Australia, the acceptable flood capacity (AFC) for a High AHazard Category dam is the PMP DF (DEWS, 2013).

Xu and Benmokrane (1996) collected and analysed data on 60concrete dams that had been strengthened using post-tensionedanchors, mainly in the USA, Canada, Australia and Europe. Theyfound that most dams had been strengthened for one or more ofthe following purposes:

� increasing spillway capacity and stability relating to the PMF;� upgrading to the MCE;� upgrading dam stability relating to other conditions such asageing and deterioration;

� raising dam height related to the PMF;� raising dam height for greater storage;� remedying deficiencies in design (e.g. not allowing adequatelyfor uplift);

� stabilising concrete cracks;� strengthening dam abutments;� stabilising dam foundations; and� reinforcing lock walls or building locks into cofferdams.

Fig. 2 illustrates schematically the classical uses of post-tensioned rock anchors in stabilising concrete gravity damsagainst (a) overturning, and (b) downstream sliding. Fig. 2a showsthe main forces used in calculating the anchor tension, T, requiredto maintain moment equilibrium about the downstream toe of thedam. Fig. 2b shows the forces involved in a limiting equilibriumanalysis of one of the several possible forms of downstream sliding(USACE, 1995; Fell et al., 2005). It must be recognised that, inpractice, concrete dams located in valleys with sloped rock foun-dation abutments will behave as three-dimensional (3D) structuresand so will require 3D stability analyses (Lombardi, 2007; Bretaset al., 2012). Clearly, different analytical models from thoseshown in Fig. 2 would have to be used for the design of post-tensioned anchors for stabilising other components of the overall

Upstream waterpressure force, H

Downstream waterpressure force, H

Damweight, W

Anchortension, T

Bond length

Drained upliftpressure force, V

Upstream waterpressure force, H

Downstream waterpressure force, H

Damweight, W

Anchortension, T

Bondlength

Drained upliftpressure force, U

Uplift pressureforce, U

(a) (b)

Fig. 2. Schematic illustration of the use of post-tensioned anchors to resist (a) overturning, and (b) downstream sliding (after ANCOLD (1992) and USACE (1995)).

E.T. Brown / Journal of Rock Mechanics and Geotechnical Engineering 7 (2015) 1e13 3

dam structure such as thrust blocks for arch dams, and spillway,training wall and stilling basin structures.

Since the time of the review by Xu and Benmokrane (1996), thenumbers of concrete dams being strengthened or raised around theworld have increased significantly, although the main reasons fordoing so have remained essentially the same. In a 2007 review ofrock anchoring of North American dams over the previous 40 years,Bruce andWolfhope (2007, 2008) identified 400 relevant cases andaccessed 230 technical publications dealing with more than 200dams. By this time, the sizes of the high-capacity anchors beingused in dam engineering had increased considerably with tendonsbeing made up of several tens of 15.2 mm diameter strands, each ofwhich generally consists of seven twisted, low relaxation, hightensile steel wires. A frequently used high-capacity tendonconfiguration consists of 91 (or 92) 15.2 mm diameter strandsproviding an ultimate axial tensile force capacity of 24 MN(Aschenbroich, 2007; Cavill, 2000; Harman et al., 2010). Even largeranchors than this have been used in some cases.

3. Overview of post-tensioned anchor design

3.1. General principles

This sub-section will discuss the basic mechanics and generalprinciples on which post-tensioned rock anchor design is based.The rock mechanics and rock engineering aspects of anchor designwill be considered in more detail in Sections 4 and 5. Althoughstrictly they lie somewhat outside the rock mechanics and rockengineering emphasis of this paper, for completeness and becausethey impact on the effectiveness of the rock engineering design, anumber of important investigation, design and construction issues,including anchor stressing and testing, will be referred to briefly inSection 6.

Traditionally, the dimensioning of rock anchor systems for damshas been based on two-dimensional (2D) static limiting equilib-rium analyses of problem configurations such as those illustratedschematically in Fig. 2. From these analyses, the anchor forcesrequired to maintain stability per metre run, or at a particularlocation, can be established for particular load cases (often callednormal or usual, unusual and extreme) and the associated factors of

safety required by the Standards, Codes of Practice or Guidelinesunder which the design is being carried out (ANCOLD, 1991, 1992,2013; BC Hydro, 1995; USACE, 1995, 2005; CDSA, 1999). It isimportant to note that different load factors or factors of safety maybe required by different authorities for similar load cases. Infor-mative comparisons between a number of these approaches aregiven by Ebeling et al. (2000) and Fell et al. (2005).

More recently, linear and nonlinear numerical stress analysisapproaches have been used to calculate forces, stresses and dis-placements in the concrete of the dam, the foundation and abut-ment rock, and at interfaces, and when assessing the dynamicstability of dams under earthquake loading (Alonso et al., 1996; Yuet al., 2005; Bureau et al., 2007; Scott and Mills-Bria, 2008; Lemos,2011, 2014; Chopra, 2012). Some Standards, Codes of Practice andGuidelines now require the use of limit state approaches or ofpartial, rather than overall, factors of safety (Merrifield et al., 1997;Herweynen, 1998; ANCOLD, 2013; Farrell, 2013). However, it hasbeen recognised recently that the partial factor, limit state designapproach used in Eurocode 7 (CEN, 2004), for example, may not beapplicable to a range of rock engineering problems in which someof the uncertainty in parameter values is epistemic rather than fullyaleatory as is assumed in the Eurocode approach (Bedi and Orr,2014; Harrison, 2014; Lamas et al., 2014). Increasingly, reliability,risk-based, probabilistic and fragility methods of dam analysis andassessment are being used in rock anchor design for dams andother applications (Ellingwood and Tekie, 2001; Phoon et al., 2003;Barker, 2011; Westberg Wilde and Johansson, 2013). Further dis-cussion of these approaches is outside the purpose and scope of thispaper.

3.2. Principal modes of failure of grouted, post-tensioned anchors

As well as providing the resistance or stabilising forces requiredfor the purposes referred to at the beginning of Section 2, groutedpost-tensioned anchors themselves must be able to resist the fourprincipal modes of applied tension-induced failure illustrated inFig. 3:

� Mode A e steel tendon tensile failure.� Mode B e groutetendon bond or interface failure.

Bars pullout of grout

Bars break

Slip surfaceFailuresurface

(a) Steel. (b) Steel-grout interface.

(c) Grout-rock interface. (d) Rock mass uplift.

Fig. 3. Principal modes of failure of grouted rock anchors under applied axial tension.(a) Mode A e steel tendon tensile failure; (b) Mode B e groutetendon bond orinterface failure; (c) Mode C e rockegrout bond or interface failure; and (d) Mode D e

rock mass uplift failure (Pease and Kulhawy, 1984).

E.T. Brown / Journal of Rock Mechanics and Geotechnical Engineering 7 (2015) 1e134

� Mode C e rockegrout bond or interface failure.� Mode D e shear or uplift failure within the surrounding rockmass.

Following Kim and Cho (2012), if the ultimate tensile load ca-pacities of an anchor for failure Modes A, B, C and D are Qtu, Qtgu,Qrgu and Qru, respectively, then the ultimate tensile capacity of theanchor, Qu, will be the minimum of these four values, i.e.

Qu ¼ min��Qtu; Qtgu; Qrgu; Qru

�� (1)

In addition to these four major modes of failure under appliedtension, for large-scale post-tensioned rock anchors of the typeillustrated in Fig.1, it is necessary to consider the possibility of shearfailure at the internal and external interfaces between the groutand the corrugated sheathing providing a layer of corrosion pro-tection. In the usual case, the depth of the corrugations in thesheathing provides an adequate degree of interlock.

In design practice, it is a common procedure to carry out designcalculations to select the length of anchor embedment required toproduce pre-determined factors of safety against failure Modes B, Cand D. The design length of embedment is then selected as thelargest of these values (USACE, 2005). In most practical cases it isfound that Mode C is more critical than Mode B.

The essential purpose of the remainder of this paper will be toreview the rock mechanics and rock engineering aspects of designagainst failure Modes C and D. However, for completeness, sum-mary discussions of design against failure Modes A and B will begiven. In the discussions of failure Modes A, B, C and D to follow, asingle post-tensioned anchor will be generally considered. It mustbe recognised, however, that in dam engineering practice, anchorsare usually used in relatively closely-spaced rows and sometimes inmultiple rows. The interactions between adjacent anchors, partic-ularly in the Mode D case, must be taken into account in designcalculations.

3.3. Design against tendon tensile failure (Mode A)

In Mode A failure, the applied axial tensile stress exceeds theyield and, ultimately, the ultimate tensile strength of the steel in thetendon. If At is the cross-sectional area of steel in the tendon and stuis the ultimate tensile strength of the steel, then the ultimate tensilecapacity is given by

Qtu ¼ stuAt (2)

This value is sometimes referred to as the minimum breakingload (MBL) (ANCOLD, 1992). In practice, it is usual to define thedesignworking load (WL) as a proportion of theMBL, often taken as60%e65% in Australia. During installation of the anchor, it is com-mon practice to test load the anchor and fittings beyond the normalWL (for example, up to 78%e80% MBL) and to “lock-off” the loadwith sufficient allowance above the WL (for example, to 68%e72%MBL) to allow for subsequent load losses caused by creep, relaxa-tion and draw-in (ANCOLD, 1992). This is one of the areas in whichdifferent terminologies may be used in different countries and bydifferent authorities.

For the large, high-capacity, post-tensioned anchors now beingused for concrete dams, it is unusual for Mode A failure to be acontrolling feature of the design. However, as will be discussedbriefly in Section 6, several other factors which are beyond thescope of this paper have to be taken into account in the detaileddesign, fabrication, installation, stressing and monitoring of theanchors.

3.4. Design against groutetendon bond or interface failure(Mode B)

The shear resistance developed at the groutetendon interfacearises from adhesion, friction and mechanical interlock betweenthe grout and the tendon. On the initial application of the axialtensile load to the anchor, shear failure at the groutetendoninterface is resisted by adhesion and interlocking. Then asdisplacement increases, these components of shear resistance maybe overcome at points along the bond length and friction thenmakes the major contribution to shear resistance (Kim and Cho,2012). Because of the difficulty of distinguishing between andevaluating these components of shear resistance, it is commonpractice to calculate the groutetendon shear resistance as

Qtgu ¼ 2prtZlbtg

0

stguðzÞdz (3)

where rt is the radius of the steel tendon, lbtg is the length of thegroutetendon bond, and stgu(z) is the shear resistance generated atdistance z along the groutetendon interface where 0 � z � lbtg.

It is often assumed that the mobilised shear resistance, stgu, isconstant over the groutetendon interface length, lbtg, greatlysimplifying the calculation of Qtgu. It is often further assumed thatthe constant value of stgu depends on the composition and surfaceproperties of the tendon and the compressive or shear strength ofthe grout. Littlejohn and Bruce (1977) and Littlejohn (1993), amongothers, provided presumptive values of stgu for a range of condi-tions. Most Codes of Practice or Standards stipulate maximumallowable values of bond stress for different types of tendon andgrout, generally in the range 1.0e3.0 MPa. In practice, if the tendonWL is pre-determined, the groutetendon bond length required togenerate a particular factor of safety for a given bond strength canbe calculated readily from a simplified version of Eq. (3). It issometimes assumed that consideration of groutetendon bond

E.T. Brown / Journal of Rock Mechanics and Geotechnical Engineering 7 (2015) 1e13 5

failure is not necessary because consideration of the rockegroutbond failure (Mode C) alone will produce a more than adequatetendon embedment length (Littlejohn and Bruce, 1977).

A number of detailed investigations have demonstrated that thesimplifying assumptions made using the approach outlined in thepreceding paragraphs are rarely justified. For example, several au-thors have shown that the groutetendon interface shear strengthdepends on the normal confining pressure and stiffness, theroughness of the tendon, whether or not the cement in the grout isexpansive, and the grouted bond length (Benmokrane et al., 1995;Barley, 1997; Jarred and Haberfield, 1997).

The recorded influence of the grouted bond length probablyreflects the now widely accepted finding that the distribution ofshear stress along the grouted length is far from uniform, tending todecay exponentially from the free-length value at the end of thegrouted length or proximal end, towards zero at the bottom of thegrouted length or distal end (see Fig. 4), depending on the as-sumptions made in the analysis (Coates and Yu, 1970; Farmer, 1975;Benmokrane et al., 1995; Ivanovi�c and Neilson, 2009; Liu et al.,2013). The ratio of the elastic modulus of the steel tendon, Ea, tothat of the grout, Eg (if there is a thick annulus of grout), or alter-natively of the rock, has been found to have a particularly importantinfluence on the distribution of elastic shear stress along theembedment length. As shown in Fig. 4 for the case of a fullyembedded, shallow anchor, for low modulus ratios of between 0.1and 1.0 for stiffer grouts and rocks, the stress distribution ismarkedly non-uniform, but as this ratio increases in softer groutsand rocks, the stress distribution becomes more closely uniform(Coates and Yu, 1970; Liu et al., 2013).

In practice, the possibility must be considered that de-bondingwill occur at the more highly stressed proximal end of thebonded length (the top in Fig. 3b), most probably during pre-stressing (Benmokrane et al., 1995), resulting in a modification tothe elastic stress distribution as illustrated schematically in Fig. 4for the Ea/Eg ¼ 0.1 case. Distributions of shear stress of the typesillustrated in Fig. 4 have been obtained analytically and numeri-cally, and measured in a range of instrumented laboratory and fieldtests on rock bolts, cable bolts and rock anchors (Kaiser et al., 1992;Benmokrane et al., 1995; Hyett et al., 1995; Woods and Barkhordari,1997; Ivanovi�c and Neilson, 2009). The stress distribution has alsobeen found to vary with imperfect bonding and when a

0 0.1 0.2 0.3 0.4 0.5

1

2

3

4

5

6

z/r

τ/ρ

E /E =1.0

E /E =10.0

E /E=0.1

De-bonding

ρ

τ

r

z

0

Fig. 4. Distribution of elastic shear stress along the grouteanchor interface (adaptedfrom Coates and Yu (1970)).

discontinuity crosses the tensioned tendon or bolt (Zou, 2004; Zhaoand Yang, 2011). A number of authors have shown how the non-uniform distribution of shear stress along the anchor length,including the effects of de-bonding, may bemodelled by piece-wiselinear shear stress distributions (Jarred and Haberfield, 1997;Woods and Barkhordari, 1997; Ivanovi�c and Neilson, 2009; Renet al., 2010).

4. Design against rockegrout interface failure (Mode C)

4.1. The standard approach

In an analogous manner to the groutetendon interface, theshear resistance at the rockegrout interface is developed byadhesion, friction and mechanical interlock with friction playingthe major role after the other components have been overcomethrough initial relative axial displacement. As with the groutetendon interface, the ultimate rockegrout axial shear resistance iscommonly evaluated as

Qrgu ¼ 2prgZlbrg

0

srguðzÞdz (4)

where rg is the outside radius of the grouted annulus around thetendon, lbrg is the length of the rockegrout bond, and srgu(z) is theshear resistance generated at distance z along the rockegroutinterface.

Again, in common with design against groutebond tendonfailure, it is generally assumed that the shear resistance is distrib-uted uniformly over the rockegrout bond length, lbrg, so that theultimate shear resistance may be calculated as

Qrgu ¼ 2prglbrgsrgu (5)

where a constant value of srgu is assumed. Many Standards andCodes of Practice indicate that it is required, or at least preferable,that the value of srgu used in design be based on the results of pull-out tests of trial anchors installed at the site (see Section 6 below).However, it is still often selected on the basis of the rock type andcondition using tables of presumptive values generally derivedfrom those first published by Littlejohn and Bruce (1975e76, 1977).Table 1 is a condensed version of the table given by Littlejohn (1992,1993) in which the sources of Littlejohn’s entries have beenomitted. As shown in Table 1, working bond values are lower thanultimate values. Commonly, theworking rockegrout shear strengthis assumed to be approximately 10% of the uniaxial compressivestrength (UCS) of the rock up to a maximum of 4.2 MPa. In somecases, the value is based on the grout compressive strength. Barley(1988) also estimated rockegrout bond strengths from the instal-lation and testing of 10,000 anchors in a wide range of rock con-ditions in the United Kingdom.

This standard approach which has been used in several coun-tries for several decades suffers from a number of deficiencies to beoutlined in the following sub-section.

4.2. Deficiencies in the standard approach

Deficiencies in the standard simplified approach to designagainst rockegrout interface failure have been found to include:

� a uniform shear stress along the rockegrout interface isassumed as discussed in Section 3.4 for the tendon-grout bond.As noted by Bruce (1997) in a review of the stabilisation ofconcrete dams by post-tensioned anchors in the U.S.A., this

Table 1Some rockegrout bond values recommended for use in design (after Littlejohn andBruce (1975e76, 1977); Littlejohn (1992, 1993)).

Rock type Workingbond (MPa)

Ultimatebond (MPa)

Factor of safety

IgneousMedium hard basalt 5.73 3e4Weathered granite 1.5e2.5Basalt 1.21e1.38 3.86 2.8e3.2Granite 1.38e1.55 4.83 3.1e3.5Serpentine 0.45e0.59 1.55 2.6e3.5Granite and basalt 1.72e3.1 1.5e2.5

MetamorphicManhattan schist 0.7 2.8 4Slate and hard shale 0.83e1.38 1.5e2.5

Calcareous sedimentsLimestone 1 2.83 2.8Chalk e Grades IeIII(N ¼ SPT inblows/0.3 m)

0.005N 0.22e1.07 2 (Temporary)

0.01N 3e4 (Permanent)Tertiary limestone 0.83e0.97 2.76 2.9e3.3Chalk limestone 0.86e1 2.76 2.8e3.2Soft limestone 1.03e1.52 1.5e2.5Dolomitic limestone 1.38e2.07 1.5e2.5

Arenaceous sedimentsHard coarse-grainedsandstone

2.45 1.75

Weathered sandstone 0.69e0.85 3Well-cementedmudstone

0.69 2e2.5

Bunter sandstone 0.4 3Bunter sandstone(UCS > 2.0 MPa)

0.6 2e2.5

Hard fine sandstone 0.69e0.83 2.24 2.7e3.3Sandstone 0.83e1.73 1.5e2.5

Argillaceous sedimentsKeuper marl 0.17e0.25

(0.45cu)3

Weak shale 0.35Soft sandstone andshale

0.1e0.14 0.37 2.7e3.7

Soft shale 0.21e0.83 1.5e2.5GeneralCompetent rock(where UCS > 20 MPa)

UCS e 30(up to amaximumvalue of1.4 MPa)

UCS e 10(up to amaximumvalue of4.2 MPa)

3

Weak rock 0.35e0.7Medium rock 0.7e1.05Strong rock 1.05e1.4Wide variety of igneousand metamorphic rocks

1.05 2

Wide variety or rocks 0.980.50.7

1.2e2.50.7 2e2.5 (Temporary)

3 (Permanent)0.69 2.76 41.4 4.2 3

15%e20% orgrout crushingstrength

3

Concrete 1.38e2.76 1.5e2.5

d

L

L/2

DL/

2Ө60 or 90° °

° °

Fig. 5. Cone geometries used in uplift capacity calculations for single tensioned an-chors (after Littlejohn and Bruce (1975e76, 1977), Hobst and Zajíc (1977) and Littlejohn(1993)).

E.T. Brown / Journal of Rock Mechanics and Geotechnical Engineering 7 (2015) 1e136

approach using a uniform shear stress and “average” bondvalues can lead to “extraordinarily and wastefully long bondzones”;

� the wide-spread use of decades old, empirically-based, pre-sumptive interface shear strengths based on rock type andcondition and, more rarely, grout compressive strength (seeTable 1);

� as with the groutetendon interface, no allowance is made forthe influence of the normal stress acting on the grouterockinterface before and during shearing, its variation over theembedment length (Barley, 1997), or the influence of groutingmethods and pressures on the normal stresses generated (Parket al., 2013);

� no recognition is taken of the progressive nature of the rockegrout bond failure process in which at least three distinct stagesmay be identified e pseudo-elastic behaviour at small de-formations, failure or de-bonding development at the rockegrout interface, and residual behaviour after larger displace-ments (Pease and Kulhawy, 1984; Park et al., 2013);

� no allowance is made for the effects of structural features suchas faults, shear zones and jointing in the rock mass or of otherlocal variations in rock strength (Dados, 1984; Zou, 2004);

� the influence of the borehole roughness and diameter, andtherefore the thickness of the grout annulus, are not considered;and

� the type of cement used in the grout can have a significant in-fluence on the shear resistance generated (Haberfield andBaycan, 1997).

In dam engineering practice, the preferred way of overcomingsome of these deficiencies is by the use of a necessarily averageinterface shear strength value established through full-scale pull-out tests on trial anchors of the anticipated design, carried out inthe rock mass concerned before the design is finalised (Scott andBruce, 1992; Feddersen, 1997; Cavill, 2000). In tests carried outfor this purpose, it is important that the test configuration isselected to ensure that the failure occurs at the rockegroutinterface.

5. Design against rock mass failure (Mode D)

5.1. The standard approach

Although it is generally found to be conservative, from a rockmechanics or rock engineering perspective, the commonly-used orstandard approach to the design of post-tensioned anchors againstrock mass failure by uplift (Mode D), is probably the least satis-factory of the design approaches discussed in this paper.

As illustrated in Fig. 5 for the case of a single anchor, the simpleststandard approach assumes that the uplift force generated by thepost-tensioned anchor is resisted by the weight of a cone of ho-mogeneous rock. It generally ignores the fact that for uplift to occur,not only the weight of the rock cone, but also the shear and/ortensile strength of the rock mass must be overcome. Depending onthe nature of the anchorage and the assumed properties of the rockmass, the cone angle and the location of the apex of the cone mayvary. Fig. 5 illustrates the commonly assumed cases in which thecone angle is either 60� or 90�, and the apex of the cone is located atthe mid-point or at the distal end of the grouted embedmentlength. Some designers may also locate the apex of the cone at the

E.T. Brown / Journal of Rock Mechanics and Geotechnical Engineering 7 (2015) 1e13 7

proximal or upper end of the bonded length. A cone angle of 60� isusually used if the rock mass is soft, heavily fissured or weathered,with an angle of 90� being used for all other rock mass conditions(Hobst and Zajíc, 1977; Littlejohn, 1993) which is generally the casefor concrete dam strengthening or stabilisation. For grouted an-chors of the type being considered here, the apex of the cone isusually taken to be at the mid-point of the grouted anchor length.This assumption with a 90� cone angle has been used in dam en-gineering at least since the 1950s (Morris and Garrett, 1956; Banks,1957).

For a general cone angle of qc (qc ¼ 60� or 90� in Fig. 5) and theapex of the cone located at the mid-point of the grouted embed-ment length, the uplift force required to overcome theweight of thecone of rock, Wc, may be calculated as

Qru ¼ 13pg tan2qc

2

�Dþ L

2

�3

(6)

where g is the unit weight of the rock, D is the depth from thesurface to the top or proximal end of the embedment length, and Lis the grouted embedment or bond length. Although it is moreconservative to use the full unit weight of the rock in this calcula-tion, in some applications in dam engineering the buoyant orsubmerged unit weight should be used. Commonly in design, therequired bond length, L, is calculated by equating the rockegroutbond resistance given by Eq. (5) to the uplift force required toovercome the weight of the cone of rock given by Eq. (6) andapplying a factor of safety, often taken to be 2.

In the author’s experience, this simple, conservative approach isgenerally used in dam engineering in the dimensioning of largepost-tensioned anchors against failure of the rock mass by uplift.However, two modifications may be made to allow more realisti-cally for the circumstances and conditions met in practice.

Firstly, for major applications such as the anchoring of concretedams in the manner illustrated in Fig. 2a and the anchoring of damtoes, spillways and training walls, anchors are generally installed inrows at relatively close spacings of a few metres. In these cases,cones such as those illustrated in Fig. 5 will overlap or interact asshown conceptually in two dimensions in Fig. 6a. In this case, thecalculation of the weight of the cone given by Eq. (6) may bereplaced by a simple approximate 2D calculation assuming atriangular cross-section to give the uplift resistance available perunit length along the row of anchors as

Qru ¼ 12g

s

�Dþ L

2

�2tan

qc2

(7)

where s is the spacing of anchors along the row.An important practical case arises when the rock mass contains

sub-horizontal bedding or structural features including jointing. Inthis case, the anchorage horizons within a row of anchors may bestaggered vertically such that the tendency to uplift a volume of

(a) (b)

Fig. 6. Interaction of uplift cones in a single row of tensioned anchors. (a) A verticalsection along the row of anchors (after Littlejohn (1993)); and (b) a simplified trian-gular cross-section normal to the row (after Hobst and Zajíc (1977)).

rock defined by the one sub-horizontal plane is avoided (Xu andBenmokrane, 1996). In the writer’s experience, this practice hasbeen used when the dam is founded on igneous rock in whichsheeting jointing has developed in an incised river valley.

Secondly, in the calculations of uplift resistance in a range ofapplications, some authorities and authors seek to allow for thetensile or shear strength of the rockmass, generally through the useof assumed values of rock mass tensile strength, shear strength orcohesion (Coates, 1970; Hobst and Zajíc, 1977; Anon, 1996; Kim andCho, 2012). The estimated values of tensile or shear resistance maybe used either instead of, or in addition to, the resistance to upliftprovided by the weight of the cone of rock. In presenting ap-proaches of this type, some authors use idealised 2D representa-tions with a triangular section as shown in Fig. 6b rather than the3D cone. For example, Hobst and Zajíc (1977) gave a number ofsolutions in terms of the rock mass shear strength. FollowingCoates and Yu (1971), Kim and Cho (2012) suggested that the ten-sile resistance on the failure surface of the rock cone in Fig. 5, fr, isgiven by

fr ¼ strpD2c tan qc

2

cos qc2

(8)

where str is the tensile strength of the rockmass and Dc is the depthof the rock cone, equal to D þ L/2 in Fig. 5.

Of course, this approach begs the question of the exact physicalmeaning of the assumed parameter, str, and how it might best beestimated. In an alternative approach, Weerasinghe and Adams(1997) proposed the use of a rock mass shear strength, ratherthan a tensile strength, back-calculated from the results of pull-outtests, assuming a theoretical failure cone of the type being dis-cussed here. Clearly, the use of this approach to estimate rock massshear strength would be impracticable for the very high-capacity,large-scale anchors such as those described by Cavill (1997, 2000)now being used in dam engineering, not least because it is diffi-cult to understand how the assumed failure mechanism coulddevelop in most practical circumstances. This and related issueswill be discussed in more detail in Section 5.2 to follow.

5.2. Deficiencies of the standard approach

As with the approaches used to design against groutetendon(Mode B) and rockegrout (Mode C) bond failures discussed previ-ously, from a rock mechanics and rock engineering perspective, thecommonly-used approach to design against rock mass uplift (ModeD) failure assuming a conical uplift failure mechanism, suffers froma number of deficiencies. The major rock mechanics and rock en-gineering deficiencies will be discussed briefly below in terms ofthe implicitly assumed stress distribution imposed within the rockmass, the rock mass uplift failure mechanism, the influence of therock mass structure, and the assumed uniform values of rock masstensile and/or shear strengths.

5.2.1. Stress distribution induced in the overlying rock massIf failure of, or large deformations in, a rockmass influenced by a

single anchor or a system of post-tensioned anchors is to beassumed, knowledge is required of the distribution of stressesinduced in the rock mass by the anchor and other means. In manycases, concrete dams are constructed in or across incised valleys orgorges. In these cases, the major principal in situ stress near thesurface is likely to be oriented parallel to the valley surface. In thecases illustrated in Figs. 5 and 6, the weight of the rock and thetransfer of stress from the tensioned anchor to the rock mass mustalso be considered in calculating the distribution of stresses within

Active cone fails in shear

Monolithic displacementof fixed anchor

Shaft below cone failsthrough the rock

Tensile cracking

Surface disturbance due todisplacement of central cone

Fig. 7. Failure by uplift of a fully grouted, straight-shafted, shallow, tensioned anchor inweak mudstone (Weerasinghe and Littlejohn, 1997).

Fig. 8. Influence of rock mass structure on the uplift failure mechanism of a shallow,fully grouted, tensioned anchor (after Wyllie (1999)).

E.T. Brown / Journal of Rock Mechanics and Geotechnical Engineering 7 (2015) 1e138

the rock mass around and above the anchor(s). In many cases, therock mass can be expected to have anisotropic elastic properties. Inthe case of a deep, post-tensioned anchor loaded through a surfacebearing plate, a bulb of compressive vertical stress will be inducedin the rock mass around the anchor head, and the stress distribu-tion around the anchor embedment length at some depth can beexpected to be quite complex and non-uniform. Furthermore, itmust be expected that the final induced stress distribution will beinfluenced by weathering profiles, changes in rock type and anymajor structural features transecting the section of the rock massinfluenced by the anchor-related stresses. Because of this range ofinfluences, it is not easy to conceptualise a general pattern of stressinduced in the rock mass by a single, deep, post-tensioned anchoror by a system of deep, post-tensioned anchors that is likely to leadto a conical failure surface.

The assumption of a cone of failure discussed in Section 5.1implies that either the tensile or shear strengths of the rock mass,or both, must be overcome over the surface of the cone before upliftcan occur. If, as is usually the case, it is assumed that the shear andtensile strengths of the rock mass are constant over any givendepth, this implies, in turn, that the shear and/or tensile stressesinduced in the rock mass must reach their maxima along somecone-like surface (in the case of a single anchor). While, as will bediscussed in Section 5.2.2 below, it can be readily envisaged thatthis will occur in the case of a short anchor that is grouted to, orclose to, the surface, it is more difficult to understand why thisshould be the case when the anchor is grouted only over anembedment length, L, which is often significantly less than D, thedepth below the ground surface of the proximal end of the groutedlength. In the first instance, the distribution of induced elasticstresses could be investigated through a series of relatively simplenumerical stress analyses of sample problem configurations.

5.2.2. Rock mass uplift failure mechanismMost direct observations of the rock mass uplift failure mech-

anism of which the author is aware, were associatedwith field pull-out tests in which, almost of necessity, the anchor was short incomparison to the lengths of the large post-tensioned anchors usedin dam construction and rehabilitation projects, and the anchorwasgrouted to, or close to, the ground surface (Dados, 1984;Benmokrane et al., 1995; Carter, 1995; Weerasinghe andLittlejohn, 1997; Serrano and Olalla, 1999; Thomas-Lepine, 2012).Furthermore, in some of these cases, the test anchor was installedin near-surface, weak rock.

A number of such investigations have found that whilediscernible surface uplift extends for some distance laterally fromthe anchor borehole, the limit of “significant” uplift can be repre-sented reasonably well by a 90� cone. For example, Fig. 7 shows thefailure mechanism observed and inferred by Weerasinghe andLittlejohn (1997) for a straight shafted anchor grouted to theground surface in aweakmudstone and subjected to uplift. The testanchor was composed of a seven 15.2 mm 7-wire drawn strandtendon with nodes in the fixed anchor length to reduce the possi-bility of groutetendon failure. Weerasinghe and Littlejohn (1997)noted that the central cone at the top of the anchor was formedby rock mass failure in shear. It is suggested that the failuremechanism would be quite different if the same anchor wasinstalled in the same rock mass in a configuration such as thatshown in Fig. 5 with the relatively high values of D/L used inmodern dam engineering practice.

5.2.3. Influence of rock mass structureClearly, the structure of the rockmass will influence the shape of

the “failure” surface. Dados (1984), Wyllie (1999) and Thomas-Lepine (2012), among others, have shown how horizontal

bedding or jointing and vertical cross-jointing can have a majorinfluence on the observed uplift failure mechanism in near-surfaceanchors. Similarly, a set of persistent, inclined discontinuities canexert a controlling influence on the failure surface geometry. Ingeneral, rock masses having the main discontinuity set perpen-dicular to the anchor axis are the most suitable in which to fixanchors (Hobst and Zajíc, 1977). Fig. 8 shows some simple repre-sentations of possible influences of rock mass structure for the caseof a shallow anchor that is fully grouted to the ground surface. In anumber of the shallow anchor cases illustrated in Figs. 7 and 8, it iseasy to postulate a conical or pseudo-conical failure surface,remembering that the in situ problem is 3D and not 2D as shown inthe sketches of Figs. 7 and 8.

It appears reasonable to suggest that, in the cases of the deepanchors used in dam engineering, the near-surface rock massstructure may not exert the same immediate controlling influence,and the 90� uplift cone assumption may not be as valid, as in theshallow anchor case. In any event, the deeper the anchor, or thegreater the ratio of the anchor depth, D, to the embedment length,L, in Fig. 5, the less likely the conical rock mass uplift mechanism isto control the behaviour of the post-tensioned anchor.Weerasinghe and Littlejohn (1997) argued that, for fully groutedanchors, as anchorage depth increases, the resistance of the rockmass cone will become smaller compared to the shaft (grouterock)resistance. Numerical experiments using discrete element codesprovide perhaps the most promising means of exploring potentialfailure mechanisms of deep anchors in rock masses for which rockmass structure models or discrete fracture network (DFN) simula-tions are available (Panton et al., 2014). Ideally, numerical analysesof this type should be 3D rather than 2D.

As was noted at the end of Section 5.1, in dam engineering, thepotential influence of a continuous or near-continuous horizontalor sub-horizontal structural feature such as a bedding plane orsheeting joint can be reduced by staggering the elevations of theanchor lengths of adjacent anchors in a row. In either the shallow or

E.T. Brown / Journal of Rock Mechanics and Geotechnical Engineering 7 (2015) 1e13 9

deep anchor case, or in the case of a row of anchors as illustrated inFig. 6, it must be recognised that, as shown by a range of pull-outtests and by preliminary numerical simulations carried out byPanton et al. (2014), the rock mass uplift failure mechanismwill beprogressive.

5.2.4. Estimation of rock mass shear and/or tensile strengthsExisting design approaches using the 90� or 60� uplift cone

hypotheses, variously assume shear, cohesive and/or tensilestrengths of the rock mass which may be the presumptive values orbe back-calculated from the results of pull-out tests using a“theoretical” failure cone (Hobst and Zajíc, 1977; USACE, 1995;Weerasinghe and Adams, 1997). Clearly, these simple approachesdo not take into account the variability of the governing strengthparameters with depth and with varying local rock mass structure,or the progressive and complex nature of the rock mass failuremechanisms involved. Nor do they always allow for the influence ofthe total distribution of stresses within the rock mass. It is sug-gested that these simplistic approaches can, and should, beimproved.

5.3. Suggested alternative approaches

At the end of Section 3.1, it was noted that linear and nonlinearstatic and dynamic numerical stress analyses (Alonso et al., 1996;Yu et al., 2005; Bureau et al., 2007; Scott and Mills-Bria, 2008;Lemos, 2011, 2014; Chopra, 2012), limit state (Merrifield et al., 1997;Herweynen, 1998; ANCOLD, 2013; Farrell, 2013), reliability, risk-based, probabilistic and fragility methods (Ellingwood and Tekie,2001; Phoon et al., 2003; Barker, 2011; Westberg Wilde andJohansson, 2013) are now being used for dam design analysis andassessment. These approaches may be used when analysing theoverall stability of dams stabilised by post-tensioned anchors in themanner illustrated schematically in Fig. 2. As well as the traditionallimiting equilibrium analyses, numerical stress analysis methodsmay use continuum, equivalent continuum or discontinuummethods. As was indicated in Section 5.2.3 and has been demon-strated by Panton et al. (2014), numerical methods, particularlydiscontinuum methods used in conjunction with a structural orDFN model of the rock mass concerned, potentially provide apowerfulmeans of investigating the likely responses of rockmassesto the uplift imposed by post-tensioned anchors. Providedadequate input data are available (see Section 6.1 below), thesemethods can also allow the influence of the in situ stresses and thestresses induced in the rock mass to be evaluated more rationallyand more fully than does the standard design approach discussedin Section 5.1. However, in the author’s experience, detailed designanalyses of this proposed type are rarely carried out in practice.

Although the previous discussion concerned Mode D or rockmass uplift failure, it should also be noted that, for any given case,comprehensive numerical analyses can be used to improve themethods generally used to estimate the distribution of normal andshear stresses along tendonegrout and rockegrout interfaces andto evaluate the onset and progression of interface bond failure andslip. Although this may appear to be relatively straight-forward, forits complete numerical analysis, this problem requires the evalua-tion and input of a number of rock and grout properties, includingstiffnesses. As noted in Section 3.4, historically a significant numberof analyses of this type have been carried out for rock and cablebolts and for shallow or near-surface anchors, but to the best of theauthor’s knowledge rarely, if at all, for the large post-tensionedanchors currently being used for dam stabilisation.

As discussed in Section 5.2, there are a number of problemconfigurations for which the 60� or 90� uplift cone assumptions donot provide realistic models for use in design analysis. In a range of

other geotechnical engineering applications, including someinvolving anchored structures, the upper and lower bound theo-rems of limit state theory have been used to identify likely failuremechanisms and the associated limit loads (Sloan, 1989, 2013;Regenass and Soubra, 1997; Soubra and Regenass, 1997). In thesegeotechnical engineering applications, numerical methods, notablyfinite element methods, including large deformation finite elementmethods, have been used in conjunctionwith limit state analysis toobtain solutions to otherwise intractable problems (Sloan, 1989,2013; Wang et al., 2013). It is suggested that such an approachcould be used to good effect to identify potential rock mass upliftconditions associated with the use of large post-tensioned anchorsto stabilise or strengthen dams.

6. Other investigation, design and construction issues

6.1. Overview

The major rock mechanics and rock engineering issues associ-ated with the design of post-tensioned rock anchors for concretedams have been discussed in the preceding sections of this paper.However, in order to ensure acceptable performance of the anchorsand of the structures that they are intended to stabilise or reinforce,a range of other site investigation, design and construction issuesassociated with the anchors have to be planned and executedsatisfactorily. To discuss all of them in detail would extend thescope of this paper beyond reasonable limits. However, forcompleteness, they will be referred to briefly here. These issuesinclude:

� site investigation and characterisation;� the installation and testing of trial anchors;� grout design and grouting trials;� the fabrication, installation, tensioning and possibly re-tensioning of the anchors;

� the provision of corrosion protection to the anchors and anchorheads; and

� the in service monitoring and maintenance of anchors and theirfittings.

Many of these issues are covered by Standards, Codes of Practiceand Guidelines. Some of them will be discussed briefly below.

6.2. Site investigation and characterisation

As the author has argued elsewhere (Brown, 2011), the designand construction of large dams played a significant role in thedevelopment of rock mechanics and rock engineering knowledgeand techniques that took place in the middle decades of the 20thcentury. This applied particularly to site investigation methods andto the assessment of the mechanical properties of rocks and rockmasses, including discontinuities. In modern dam engineering,adequate site investigation and the resulting site characterisation,and geological, structural and geotechnical model developmentremain of paramount importance. In terms of the various types ofdesign analyses discussed in this paper, particular site characteri-sation requirements include:

� estimating the in situ stresses at the dam site, particularly underincised valleys;

� mapping discontinuities in the foundation rock mass anddeveloping complete 3D structural models for the geotechnicaldomains identified, preferably using a DFN approach;

� estimating rock and rock mass strengths and deformabilities;

E.T. Brown / Journal of Rock Mechanics and Geotechnical Engineering 7 (2015) 1e1310

� measuring or estimating the basic friction angles, roughnessesand normal and shear stiffnesses of persistent discontinuitieslikely to be involved in the sliding mode of failure illustrated inFig. 2b;

� establishing design values of the shear and tensile strengths ofold and new foundation rockemass concrete interfaces (Lo et al.,1991; EPRI, 1992); and

� measuring or estimating rock mass permeabilities and identi-fying significant water-bearing discontinuities in the foundation(Farinha et al., 2011).

Examples of some of the modern approaches and techniquesused to obtain data of these types are given by Brown and Marley(2008), Powell et al. (2008), Shaffner et al. (2009), Friz et al.(2011), Hencher et al. (2011) and Agharazi et al. (2012).

6.3. Anchor and grouting trials

It is essential that before the detailed design of a system of large,post-tensioned anchors is completed, trial anchors of prototypesize should be installed in the rock mass concerned and load tested.This overall process should include tests of drilling accuracy anddrill hole stability in the candidate rock mass; tests of proposedgrout mixes and grouting tests to enable suitable grouting pres-sures to be determined and the extent of the likely loss of grout intothe surrounding rock mass to be assessed; and, perhaps mostimportantly, load testing of a generally small number of trial an-chors for a range of possible purposes, including the identificationof potential failure mechanisms and, with suitable test design, theestimation of mean rockegrout interface strengths. As will be dis-cussed in Section 6.4 to follow, it is also common or requiredpractice to test load each prototype anchor on installation andsubsequently during the anchor’s service life. Examples of anchortesting procedures and results are given by Habib (1989), Scott andBruce (1992), Littlejohn (1993), Bruce (1997), Feddersen (1997) andCavill (2000).

6.4. Anchor stressing and in service monitoring

The initial anchor stressing and proof-testing, and the inspec-tion, monitoring, maintenance and re-stressing of anchors duringtheir service lives, are critically important in ensuring the satis-factory in service performance of post-stressed anchor systems. AsLittlejohn (1993) noted, “stressing is required to fulfil two func-tions. (i) To tension the tendon and to anchor it at its secure load. (ii)To ascertain and record the behaviour of the anchorage so that itcan be compared with the behaviour of control anchorages, sub-jected to on-site suitability tests.” The structural design of the an-chor stressing system, including the load cell, anchor head andbearing plate, is an important element of this undertaking(Littlejohn, 1993). As was noted in Section 3.3, during installation ofthe anchor, it is common practice in Australia to test load the an-chor and fittings beyond the normal WL (for example, up to 78%e80%MBL) and to “lock-off” the load with sufficient allowance abovethe WL (for example, to 68%e72% MBL) to allow for subsequentload losses caused by creep, relaxation and draw-in (ANCOLD,1992). Following this initial stressing, it is necessary to protectthe anchor head against corrosion while ensuring that it remainsaccessible for subsequent inspection and re-stressing (Littlejohnand Mothersille, 2007).

The volume edited by Littlejohn (2007) contains a wide range ofpapers on the in service inspection, maintenance andmonitoring ofground anchors and anchored structures, including dams(Aschenbroich, 2007; Wolfhope et al., 2007; Zicko et al., 2007).

7. Conclusions

High-capacity, post-tensioned anchors have found wide-spreaduse, originally in initial dam design and construction, and morerecently in the strengthening and rehabilitation of concrete dams tomeet modern design and safety standards. Despite the advancesthat have been made in rock mechanics and rock engineeringduring the almost 80 years in which post-tensioned anchors havebeen used in dam engineering, the author’s reading of the litera-ture, and his own practical experience in Australia, suggest thatsome aspects of the rock mechanics and rock engineering design ofrock anchors for dams have changed relatively little over the last 30or 40 years. This applies, in particular, to the calculations usuallycarried out to establish the grouted embedment lengths requiredfor deep, post-tensioned anchors. These calculations usually makesimplified assumptions about the distribution and values of rockegrout interface shear strengths, the shape of the volume of rocklikely to be involved in uplift failure under the influence of a systemof post-tensioned anchors, and the mechanism of that failure. Theresulting designs are generally conservative. While this is under-standable for important structures like dams for which publicsafety is a major consideration, in some cases, the degree ofconservatism is considered to be excessive and to represent poorengineering practice.

It is concluded that the aspects of rock mechanics and rockengineering design of large, post-tensioned rock anchors for damsof major concern here, the rockegrout bond and the uplift failuremechanism, can be significantly improved bymaking greater use ofmodern, comprehensive, numerical analyses in conjunction with3D models of the rock mass structure, realistic rock and rock massproperties, and the results of prototype anchor tests in the rockmass concerned.

Conflict of interest

The author has no known conflict of interest associatedwith thisreview paper.

Acknowledgements

The author wishes to thank thosewho gave him the opportunityto become involved in dam engineering at a relatively late stage ofhis career, and those with whom he has worked on projects anddiscussed the issues addressed in this paper. They include: BrianCooper, Peter Foster, Tim Griggs, Richard Herweynen, Mike Marley,Peter Richardson and Richard Rodd. He would also thank themanagement and Principals of the Brisbane office of Golder Asso-ciates for facilitating his work in dam engineering and supportingthe preparation of this paper; Mike Marley and Rob Morphet forinternally reviewing of the paper; Guy Green for preparing thedrawings; and Jo-Anne Sandilands for her word processingassistance.

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E.T. Brown / Journal of Rock Mechanics and Geotechnical Engineering 7 (2015) 1e13 13

E.T. (Ted) Brown is a graduate of the Universities of Mel-bourne (BE 1960; MEngSc 1964), Queensland (PhD 1969)and London (DSc(Eng) 1985). He began his engineeringcareer in the then State Electricity Commission of Victo-ria’s brown coal mining operations in 1960. After severalyears at what became James Cook University in Townsville,he joined the staff of the Royal School of Mines, ImperialCollege of Science and Technology, London, in 1975. Hewas appointed Professor of Rock Mechanics in 1979, andserved as Dean of the Royal School of Mines (1983e1986)and Head, Department of Mineral Resources Engineering(1985e1987). In October 1987, Professor Brown returnedto Australia as the University of Queensland’s first full-time Dean of Engineering. He became Deputy Vice-

Chancellor of the University in October 1990 and Senior Deputy Vice-Chancellor inJanuary 1996. Since retiring early from that position in early 2001, he has worked asa Senior Consultant to Golder Associates Pty Ltd. and had served on a number of

Boards. Professor Brown has wide international experience as a researcher, teacher,consultant and writer on rock mechanics and its applications in the mining, civil engi-neering and energy resources industries. He served as Chairman of the BritishGeotechnical Society in 1982 and 1983, and as President of the International Societyfor Rock Mechanics from 1983 to 1987. He was elected an International Fellow ofThe Royal Academy of Engineering, UK, in 1989, and a Fellow of the Australian Acad-emy of Technological Sciences and Engineering in 1990. In 2001, he was appointed aCompanion in the Order of Australia for “services to the engineering profession as aworld expert in rock mechanics and to scholarship through promotion of the highest aca-demic and professional standards.” He was awarded the Consolidated Gold Fields GoldMedal of the then Institute of Mining & Metallurgy in 1984; a Centenary Medal by theAustralian Government in 2003 “for service to Australian society in mining and civil en-gineering”; the John Jaeger Memorial Award of the Australian Geomechanics Society in2004; the President’s Award of the Australasian Institute of Mining & Metallurgy for2006; the International Society for Rock Mechanics’ highest honour, the Müller Award,in 2007; the SME Rock Mechanics Award in 2010; and the Douglas Hay Medal of theInstitute of Metals, Minerals & Mining in 2013.