Shear strength criteria for rock,rock joints,rock fill and rock masses:Problems and some solutions

Nick Barton

Nick Barton&Associates,Oslo,Norway

1.Introduction

Non-linear shear strength envelopes for intact rock and for(non-planar)rock joints are the reality,but traditional shear test interpretation and numerical modelling in rock mechanics has ignored this for a long time.The non-linear Hoek-Brown(H-B)criterion for intact rock was eventually adopted,and many have also used the non-linear shear strength criterion for rock joints,using the Barton and Choubey(1977)wall-roughness and wall strength parameters JRC (joint roughness coefficient) and JCS(joint compressive strength).

Non-linearity is also the rule for the peak shear strength of rock fill.It is therefore somewhat remarkable why so many are still wedded to the ‘c+σntanφ’linear strength envelope format.Simplicity is hardly a substitute for reality.Fig.1 illustrates a series of simple strength criteria that predate H-B,and that are distinctly different from Mohr-Coulomb(M-C),due to their nonlinearity.

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The actual shear strength of rock masses, meaning the prior failure of the intact bridges and then shear on the fractures and joints at larger strains,is shown in Fig.1(units of σ1and σ2are in MPa).

2.Intact rock

The three-component based empirical equations(using roughness,wall strength and friction)shown in Fig.1 were mostly derived in Barton(1976).The similarity of shear strength for rock joints and rock fill was demonstrated later in Barton and Kjærnsli(1981).

At the time of this mid-seventies research by the writer,it was recognized that the shear strength envelopes for intact rock,when tested over a wide range of confining stress,would have marked curvature,and eventually reach a horizontal stage with no further increase in strength.This was termed the ‘critical state’,and the simple relation σ1=3σ3suggested itself,as illustrated in Fig.2.

The very important findings of Hajiabdolmajid et al.(2000)are summarized briefly by means of the six figures assembled in Fig. 15The demonstrated shortcomings of continuum modelling with‘c plus σntanφ’shear strength assumptions should have alerted our profession for change already twelve years ago,but deep-seated beliefs or habits are traditionally hard to change(Barton,2011).

The curvature of peak shear strength envelopes is now more correctly described,so that few triaxial tests are required and need only be performed at low confining stress,in order to delineate the whole strength envelope. This simplicity does not of course apply to M-C,nor does it apply to non-linear criteria including H-B,where triaxial tests are required over a wide range of confining stress,in order to correct the envelope,usually to adjust to greater local curvature.

Singh et al.(2011)basically modified the M-C criterion by absorbing the critical state defined in Barton (1976), and then quantifying the necessary deviation from the linear form,using a large body of experimental test data.

Singh and Singh (2012) have developed a similar criterion for the shear strength of rock masses, with σcfor the rock mass potentially based on the simple formula 5γQc1/3(where Qc=Qσc/100(MPa)).The rock density is γ,and Q is the rock mass quality(Barton et al.,1974),based on six parameters involving relative block size,interblock friction coefficient and active stress.

When modelling a rock mass in a 2D representation,as illustrated,it is clear that deformation modulus,Poisson’s ratio,shear and tensile strengths,and density will figure as a minimum in both models.In the case of the additional representation of the jointing,one will in the case of UDEC-BB also specify values of JRC,JCS and φrfor the different joint sets, paying attention also to the spacing of cross-joints so that relevant ranges of block sizes Lnare specified,in relation to the usually smaller scale L0size of blocks or core pieces tested when characterizing the site(L0and Lnare the lab-scale and in situ scale block sizes).

Fig.2.Critical state line defined by σ1=3σ3was suggested by numerous high pressure triaxial strength tests.Note the chance closeness of the unconfined strength(σc)circle to the confining pressure σ3(critical)(Barton,1976).Note that‘J’represents jointed rock.The magnitude of φ cis 26.6° when σ1=3σ3.

3.Shear strength of rock joints

Recent drafts of the ISRM suggested methods for testing rock joints,and widely circulated errors on the Internet and in commercial numerical modelling software, caused the writer to spend some time on the topic of shear strength of rock joints,in his 6th Müller Lecture(Barton,2011).Problems identified included exaggeration of ‘cohesion intercept’in multi-stage testing,and continued use of φbin place of φr,thirty- five years after φrwas introduced in a standard equation for shear strength.

An estimate of the mobilized dilation angle d0n(mob)for adding to the joint angle β,is as follows:

Following the tests on 130 fresh and slightly weathered rock joints(ten of which are shown in Fig.3),the basic friction φbwas replaced by φr,which may be several degrees lower.This occurred in 1977,and was unfortunately overlooked/not read by the chief supplier of the Internet with his version of rock mechanics.

Due to the dominance of this ‘downloadable rock mechanics’,there have been a significant number of incorrectly analyzed rock slopes,and incorrectly back-calculated JRC values in refereed Ph.D.studies,not to mention a number of refereed publications with incorrect formula,due to failure to read outside the downloaded materials.

The reconstructed shearing events shown in Fig.4 were derived from specific tension fractures with the(two-dimensional,2D)surface roughness as shown,and displaced and dilated as measured in the specific direct shear tests.These tests on tension fractures were performed in 1968,and represented the forerunner of the non-linear criterion shown in Fig.4(#3).

In 1971(Ph.D.studies of the writer),the ‘future’‘JRC’had the value 20,due to the roughness of tension fractures,and the ‘future’‘JCS’was merely the uniaxial strength of the(unweathered)model material.For the same reason of lack of weathering,the ‘future’φrat this time was simply φb.

Fig. 5 illustrates the form of the third strength criterion shown in Fig.4(top).It will be noted that no cohesion intercept is intended.It will also be noted that subscripts have been added to indicate scale-effect(reduced)values of joint roughness JRCnand joint wall strength JCSn.This form is known as the Barton-Bandis criterion.Its effect on strength-displacement modelling is shown later.

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The scale-effect correction by Barton and Bandis(1982)is illustrated by three peak shear strength envelopes in Fig.5.It will be noted that the peak dilation angles vary significantly. This is important when transforming principal stresses to normal and shear stresses that act on a plane.This topic will be discussed later.

Recent drafts and earlier versions of the ISRM suggested methods for shear testing rock joints have suggested multi-stage testing of the same sample,to increase the numbers of test results when there are insufficient samples.Naturally,the first test is recommended performed at low stress to minimize damage.Successive tests are performed at higher normal stress, using the same sample,reset in the ‘zero-displacement’ position. Since there will be a gradual accumulation of damage,there is already a ‘built-in’tendency to reduce friction(and dilation)at higher stress,and therefore to increase the apparent cohesion intercept(if using M-C interpretation).These problems are accentuated if JRC is high,and JCS low and normal stress high in relation to JCS,therefore causing more damage during each test.

A further tendency to rotate the ‘peak’strength envelope clockwise(and exaggerate an actually non-existent M-C cohesion)is the frequent instruction to preload each sample to a higher normal stress.Barton(2007)(following Barton,1971)showed that this causes over-closure,and higher resulting shear strength,especially in the case of rough joints.We need to be concerned here(extracted from Barton,2007):

Fig.3.A simple joint-roughness(JRC)based criterion for peak shear strength.Ten typical samples are shown,together with their roughness profiles.The Barton and Choubey(1977)criterion has the form shown in Fig.4(third criterion listed).

Thermal effects in future nuclear waste repositories may further accentuate over-closure,due to an additional thermal effect:roughness profiles ‘remember’the warmer/hotter initiation temperature,and fit together better when heated.The rougher joints may remain closed when cooled as they then have some tensile strength and much increased shear strength.Smoother longer joints will then open in preference and disqualify conventional-behaviour based designs.These effects have been seen to compromise expected results of URL(underground research lab)in situ experiments,but are so far ignored in codes-also in UDEC-BB-and in HLW(high-level waste)design.

Fig.4.The(third)non-linear shear strength criterion for rock joints was developed first from(unweathered)tension fractures,and had φbin place of φr.The sheared replicas of rough tension fractures are sheared and dilated as tested(Barton,1971,1973).

The maintenance of the above described multi-stage testing procedures for rock joints has inadvertently prolonged the artificial life support of cohesion,affecting numerical modelling and countless thousands of consultants’ reports and designs.

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Some people have of course questioned the use of rock joint‘cohesion’in rock slope design,even in large scale open pit design,and ‘to be on the safe side’they ignore cohesion.This is safe but expensive,as with the above two tendencies to rotate the strength envelope clockwise(increasing ‘cohesion’and reducing‘friction’),the resulting ‘safe’friction angle may be far too conservative,and probably joint continuity is already assumed to be too high.

Fig.5.The scale-effect corrected form of the non-linear Barton(1973)strength criterion,from Barton and Bandis(1982),following modification with φrby Barton and Choubey(1977).

4.Pre-peak,post-peak shear strength

Fig.6 illustrates the strength-deformation-stiffness model used in the Barton-Band is constitutive law for rock joints.Friction is mobilized just before roughness and dilation are mobilized.After peak shear strength,JRC(and JRCn)is gradually destroyed.One should note the ‘impossibility’of reaching residual strength.The magnitude of φris illustrated in Fig.7.This important parameter can be estimated by the index tests shown in Fig.8.This figure shows a series of index tests for characterizing the strength parameters needed to explain the non-linearity and scale-dependence of shear strength.Tilt tests are shown in Fig.9.

5.Shear strength of rock fill interfaces

Fig.1 showed that there were similarities between the shear strength of rock fill and that of rock joints.This is because they both have ‘points in contact’,as shown in Fig.10,i.e.highly stressed contacting asperities or opposing stones.In fact these contacting points may be close to their crushing strength,such that similar shear strength equations apply:

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(1) τ/σn=tan[JRC·log10(JCS/σn)+φr]applies to rock joints.(2) τ/σn=tan[R·log10(S/σn)+φb]applies to rock fill.

主谓不一致问题也是较低级错误，但还是不可避免地出现。The Eggshell Bronzes Carved with Patterns was rare and excellent这句话的主语是复数，但是谓语却用了单数，所以应该修改为The Eggshell Bronzes Carved with Patterns were rare and excellent。

(3) τ/σn=tan[JRC·log10(S/σn)+φr]might apply to interfaces.

(1)Recognition of the need to improve the M-C and other(nonlinear)shear strength criteria for the intact strength of rock has led researchers at the University of Roorkee to incorporate a simple critical state concept for rock,and thereby delineate the necessary deviation from linear M-C criterion,in order to model correct curvature of the strength envelope.

Because some dam sites in glaciated mountainous countries like Norway,Switzerland,Austria have insufficient foundation roughness to prevent preferential shearing along the rock fill/rock foundation interface,artificial‘trenching’is needed.Various scales of investigation of interface strength have been published.These were analyzed in unpublished research performed by the author,and can be summarized by the data points plotted in Fig.12.

Fig.6.The JRCmobilizedconcept developed by Barton(1982)allows the modelling of strength-deformation-dilation trends,as shown in Fig.7.Note that ‘i’changes with the normal stress.

Fig.7.With scale effects caused by increasing block size accounted for(see input data in the inset),we see that laboratory testing,especially of rough joints,may need a strong adjustment(down-scaling)for application in design(Barton,1982).

Fig. 13 illustrates real examples of these two categories of shearing,in which the ‘weakest link’determines the mode of sliding:whether the interface is smooth enough and the particles big enough to prevent good interlock(JRC-controlled),or the opposite R-controlled behaviour, with preferential failure within the rockfill.

Fig.8.Direct shear testing and typical results are shown in the first(left-hand)column.Tilt tests for JRC and φb(and conversion to φr)are shown in the second column,(also see Fig.9),and Schmidt hammer testing for r(weathered joint)and R(unweathered core stick)are shown in the third column.More direct roughness(JRC)measurement is shown in the fourth column,using the amplitude/length(a/L)method,or brush-gauge recording.The a/L method is simple to interpret.

6.Numerical modelling of rock masses

It has been claimed-correctly-that rock masses are the single most complex of engineering materials utilized by man.We utilize rock masses for purposes as diverse as road, rail and water transport tunnels,dam site location,oil and gas storage,food storage and sports facilities in caverns,and we are heading for final disposal of high-level nuclear waste.

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Fig.9.Tilt testing of large diameter core and sawn blocks.Note Schmidt hammer,and roughness-measurement brush gauge.

Fig.10.Peak shear strength estimates for three categories of asperity or point-to point contact. As seen in Fig. 11, it is possible to test as-built rock fill, if the tilt-testing box is of large enough dimensions to take the compacted rock fill,from the next‘lift’.

The complexity may be due to variable jointing,clay- filled discontinuities,fault zones,anisotropic properties,and dramatic water inrush and rock-bursting stress problems.Nevertheless we have to make some attempt to represent this complexity in models.Two contrasting approaches(to a simple case)are shown in Fig.14.

Fig.11.Tilt testing of as-built rock fill,as suggested in Barton and Kjærnsli(1981),with performance of ten tests at a rock fill dam in Italy.The tilt-shear box is 5m×2m×2m.

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It is clear that the shear strength of the jointed model will be dominated by ‘the weakness’of its jointing.Equivalent continuum values of shear strength will be assigned in the case of the continuum representation.It is here that the problems begin.The limitations of M-C,H-Band‘cplusσntanφ’are likely to be observed.Attempts to model ‘break-out’ phenomena such as those illustrated in Fig.15 are not especially successful with standard M-C or H-B failure criteria,because the actual phenomena are not following our long-standing belief in ‘c plus σntanφ’.The reality is degradation of cohesion at small strain and mobilization of friction( first towards peak,then towards residual)which occur at larger strain.We register closure or squeezing,and also can measure it,as an apparent radial strain.In reality,it may be a tangential strain-related failure phenomenon.

An extensive recent study by Singh et al.(2011)in Roorkee University involving re-analysis of thousands of reported triaxial tests,including their own testing contributions,has revealed the astonishing simplicity of the following equality:σc≈σ3(critical)for the majority of rock types:in other words,the two Mohr circles referred to in Fig.2 are touching at their circumference.This is at once an ‘obvious’result and an elegantly simple result,and heralds a new era of triaxial testing.

Rock masses actually follow an even more complex progression to failure,as suggested in Barton and Pandey(2011),who recently demonstrated the application of a similar ‘c then σntanφ’modelling approach,but applied it in FLAC3D,for investigating the behaviour of multiple mine-stopes in India.A further break with convention was the application of peak ‘c’and peak ‘φ’estimates that were derived directly from mine-logged Q-parameters,using the CC (cohesive component) and FC (frictional component)parameters suggested in Barton(2002).For this method,an estimate of UCS(uniaxial compressive strength)is required,as CC and FC are derived from separate ‘halves’of the formula for Qc=Qσc/100(The Q formula is shown below Fig.16,where empirically derived Qc-VP-M inter-relationships are shown).

The two or three classes of discontinuities (natural and induced)involved in pre-peak and post-peak rock mass failure will tend to have quite different sets of shear strength properties.For instance,the new stress-induced failure surfaces,if described with JRC,JCS and φr,might have respective numbers(at small scale)like 18-22,100-150MPa and 30°-32°(i.e.rough and unweathered and strongly dilatant),compared to perhaps 4-8,50-100MPa and 27°-29°for potential joint sets,or perhaps Jr/Ja=(1-2)/4 for any clay coated discontinuities,that might also be involved in the post-peak shear strength behaviour of the rock mass.Shear strength description using Jr/Jais from the Q-system(Barton et al.,1974;Barton,2002),which is shown in Fig.A.1.in Appendix A.

Fig.12.The results of interface/rock fill and interface/sand(and gravel)direct shear tests can be separated by means of the ratio a/d95,into R-controlled and JRC-controlled categories.

Fig.14.Continuum and discontinuum modelling approaches to the representation of a rather uncomplicated,though anisotropic rock mass.The increased richness and reality of representing the potential behaviour of jointing,even if exaggerated in 2D,is clear to see.

The dilatancy obviously reduces strongly between these three groups of discontinuities.Furthermore,each of the above has the features that begin to resist shearing at considerably larger strains/deformations than is the case for the also strongly dilatant failure of the ‘intact bridges’.Why therefore are we adding‘c and σntanφ’in ‘continuum’models,making them even poorer representations of the strain-and-process-sensitive reality?

Fig.13.Four examples of a/d95that demonstrate either preference for interface sliding or preference for internal shearing in the rock fill.This can be checked(at low stress)by tilt-testing.

Input data obtained via Hoek and Brown and GSI(GSI=RMR-5)formulations that obviously ignore such complexity and reality,since not representing rock fracture and joint strength,nevertheless consist of remarkably complex algebra(e.g.Table 1)in comparison to the more transparent formulae for discontinuum codes,where JRC0,JCS0,φr,L0and Lnand use of Barton-Bandis scaling equations are sufficient to develop the key joint strength and joint stiffness estimates.

A demonstration of the simpler,Q-based continuum-model‘cohesive component’(CC)and ‘frictional component’(FC)for a variety of rock mass characteristics is given in Table 2.Low FC needs more bolting,while low CC needs more shotcrete,even local concrete linings.These are semi-empirically based ‘halves’of the Q-formula,which seem to be realistic.

These much simpler Q-based estimates have the advantage of not requiring software for their calculation-they already exist in the Q-parameter logging data,and the effect of changed conditions such as clay- fillings,or an additional joint set can be visualized immediately.This is not the case with Eqs.(2)and(4)in Table 1.

An important part of the verification of this mine stope modelling by Pandey,described in Barton and Pandey(2011),was the comparison of the modelling results with the deformations actuallymeasured with pre-mining pre-installed MPBX(extensometer)arrays,and cross referencing with empirical formulations for deformation,which are shown in Fig.17.All three sources of deformation(measured,modelled,empirical)showed good agreement(see Barton and Pandey,2011).

Table 1The remarkable complexity of the algebra for estimating c’ and φ’ with Hoek-Brown formulations is contrasted with the simplicity of equations derived by‘splitting’the existing Qcformula into two parts,as described in Barton(2002)(Qc=Qσc/100,with σcexpressed in MPa).

Fig.15.Top:The Canadian URL mine-by break-out that developed when excavating by line-drilling,in response to the obliquely acting anisotropic stresses.This is followed by an important demonstration of unsuccessful modelling by ‘classical methods’given by Hajiabdolmajid et al.(2000).They followed this with a more realistic degradation of cohesion and mobilization of friction in FLAC.

Table 2Illustration of parameters CC(MPa)and FC(°)for a declining sequence of rock mass qualities,with simultaneously reducing σc(MPa).Estimates of VP(km/s)and Em(GPa)are from Fig.16,whose derivation was described in Barton(2002).

Recent reviews of pre-excavation modelling for cavern design,and cavern performance reviews for a major metro constructor in Asia,suggest that it is wise to consult these two simple equations,when deliberating over the reality (or not) of numerical models. It is the experience of the writer that UDEC-MC and UDEC-BB modellers often exaggerate the continuity of modelled jointing(because this is easier than drawing a more representative image of the less continuous jointing,and digitizing the latter).

A common result of UDEC models with exaggerated joint continuity is that modelled deformations may be at least 10×those which are subsequently measured,and support needs have therefore been exaggerated,because of the artificial deformations.The common opinion expressed by the a priori modellers is that the a posteriori Q-system based support recommendation is not adequate.Of course they are incorrect.

Fig.16.Empirical relationships between Q values(with parameters as shown)and P-wave velocity and (static) deformation modulus M. Note corrections for increased depth or stress level, which should be applied in numerical models when significant depth variation is to be modelled(Barton,2002).

Fig.17.Two complementary figures(top figure from Barton et al.,1994),showing a total of many hundreds of tunnel monitoring data.Their source is given in Barton(2002).The central(very approximate)data trend can be described by the simplest equation that is possible in rock engineering.See Table 3,which also shows a more accurate version for checking the probable validity(or need for adjustment of joint representation)in numerical model results.

Table 3Empirical equations linking tunnel or cavern deformation to Q-value(from Barton,2002).In the top equation SPAN=meters(as in the vertical axes of Fig.17).In the bottom equation SPAN=mm.Both Δ and Δvare in millimeters.Vertical stress and compressive strength must have consistent units,e.g.MPa.

In fact,when the caverns are finally constructed,they may be almost self-supporting,and certainly could be permanently supported with single-shell shotcrete and(corrosion protected)rock bolting:B+S(fr),which is termed NMT to distinguish it from the much more expensive double-shell NATM(with final concrete lining).

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Note that at the record-breaking 62m span Gjøvik cavern,excavated in fresh to slightly weathered grey and red gneiss,with most frequent Qcore=10,Qcavernarch=12,the equations show 6-7mm,while the UDEC modelling(with realistic non-continuous jointing)showed 7-8mm,and the MPBX(plus surface levelling)showed 7-8mm.This was a single-shell NMT-concept drained cavern,and concrete lining was never considered(Barton et al.,1994).

7.Fundamental geotechnical error?

This paper will be concluded with a subject that has been little discussed and little publicized(Ch.16,Barton,2006).It appears to go beyond the more common distinction that we make between constant normal stress and constant normal stiffness shear testing of rock joints.

The subject of concern is the transformation of stress from a principal(2D)stress state of σ1and σ2to an inclined joint,fault or failure plane,to derive the commonly required shear and normal stress components τ and σn.If the surface onto which stress is to be transformed does not dilate,which might be the case with a(residual-strength)faultorclay- filled d is continuity,then the assumption of co-axial or co-planar stress and strain is no doubt valid.

If on the other hand dilation is involved,then stress and strain are no longer co-axial.In fact the plane onto which stress is to be transferred should even be an imaginary plane.Any non-planar rock joints and any failure planes through dense sand or through over-consolidated clay or through compacted rock fill,are neither imaginary nor non-dilatant in nature.

This problem nearly caused a rock mechanics related injury,whenBakhtar and Barton (1984) were attempting to biaxially shear diagonally fractured 1 m3samples of rock,hydrostone and concrete.The experimental set-up and various index tests are shown in Fig. 18. The sample preparation was unusual because of principal stress(σ1)driven controlled-speed tension fracturing (see triangular flat-jacks in top-left photo).This allowed fractures to be formed in a controlled manner.Fig.19 shows the stress application and related assumptions(presented in three stages).

The rock mechanics near-injury occurred when a(σ1-applying)flatjack burst at 28MPa,damaging the laboratory walls and nearly injuring the writer who was approaching to see‘what the problem was’.The sample illustrated in Fig.18(with photographer’s shoes)was transformed into ejected slabs and ejected high-pressure oil,damaging pictures on the walls,as a result of the dramatic flatjack burst.

Fig.18.Sample preparation,roughness profiling by TerraTek colleague Khosrow Bakhtar,tilt testing(at 1m3scale),lowering lightly clamped sample into test frame,LVDT instrumentation,and(a rare)sheared sample of an undulating fracture in sandstone.These 1.3m long tension fractures displayed tilt angles varying from 52°to 70°,and large-scale(Ln=1.3m)joint roughness coefficients varying from 4.2 to 10.7.

The conventional and dilation corrected stress transformation equations can be written as

where angle β is the acute angle between the principal stress σ1and the joint or failure plane.

The peak dilation angle and mobilized dilation angle can be written as

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Fig.19.(a)Test set-up,(b)stress transformation and(c)corrections for out-of plane dilation and boundary friction(Note:greased double-Teflon sheets and pairs of stainless-steel 0-30MPa flatjacks were used on all four boundaries).

Unfortunately,Hoek’s downloadable rock mechanics texts and related RockScience software represent the limit of a lot of consulting of fices contact with rock mechanics,so they have little knowledge of advances in the field that are not picked up by those who for some reason feel it their duty to feed the internet with‘free’rock mechanics.This is a dangerous and unnecessary state of affairs.

The dimensionless model for mobilization of roughness(JRC(mob))was shown in Fig.6.

8.Conclusions

The equation to be used for the interface will depend on whether there is ‘JRC’ control, or ‘R’ control. This distinction is described,and illustrated later(Fig.11.).

(2)The critical confining pressure σ3(critical)required to achieve maximum possible shear strength,where the Mohr envelope becomes horizontal,is approximately the same as the UCS for the case of most rock types.Thus σ1maximum=3σ3(critical)≈3σc.This is a surprisingly simple,though not illogical result.The result is that triaxial tests only need to be performed at low confining pressures,in order to give the complete strength envelope.This is not the case for M-C or H-B criteria.

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(3)Rock joints have had a valid non-linear strength criterion for 35years,but tradition dies hard, and linear M-C extrapolations of test data,continue to deceive many into thinking that rock joints have cohesive strength.The reality is high friction,no cohesion and strong dilation at low stress.

(4)Current multi-stage testing routines for rock joints tend to exaggerate cohesion and reduce friction. If the apparent cohesion intercept is ignored,the ultra-conservative friction angle makes for unnecessarily expensive rock slope design.

(10)There is a fundamental question mark hanging over the assumed validity of adding c and σ tanφ when trying to describe the continuum-based shear strength of rock masses.For almost 50 years since the time of Müller(1966),it has been recognized that cohesion(if existing)is broken at small strain,while friction is mobilized at much larger strain and is the remaining shear strength if displacement continues.

(6)The error of recommending φbin place of φrmay represent several degrees different strengths if joints are weathered,and results in incorrect back-calculated JRC values.This error,though now corrected,continues to affect research in universities,and publications continue to propagate this internet-age error,even in professor-monitored research and peer-reviewed publications.

(7)Rock fill placed on a rock foundation that is smoothed by glaciation may show preferential sliding along this interface.This is termed JRC-controlled behaviour.If the ratio a/d50of roughness amplitude and particle(stone)size exceeds about 7,experimental results suggest that behaviour will be R-controlled with preferential shearing through the rock fill instead.

(8)R and S replace JRC and JCS in the strength criterion for rock fill.Large-scale tilt tests can be performed with as-built compacted rock fill,using a special‘excavatable’shear box.

(9)Rock masses are generally jointed,and may be faulted,and are generally anisotropic.Nevertheless those a little external to the better educated rock mechanics communities are encouraged to model with isotropic continuum models,and are able to produce colourful and exaggerated plastic zones that adversely influence bolt-length decisions in the case of tunnel support.

一是开展省级森林小镇创建工作。为树立典型、鼓励先进，按照省林业厅工作要求，区林业局精心组织、认真开展，于2018年5月正式启动河口区森林小镇创建工作。新户镇、义和镇立足地域禀赋，积极参与创建，经省市专家评审，义和镇被山东省绿化委员会办公室、山东省林业厅授予“山东省森林小镇”荣誉称号。

(5)Incorrect download able ‘internet-age’rock mechanics has introduced an error in slope stability analyses and in research concerning the joint roughness term JRC.This is because the 35 years-old change to the residual friction angle φrin place of the unweathered basic friction angle φbwas overlooked,when ‘reproducing’the writer’s shear strength criteria.

(11)An alternative strength criterion introduced in Canadian research in about 2000,involves the degradation of cohesion followed by the mobilization of friction.This results in a much better fit to observations of stress-induced failure than M-C or H-B ‘c plus σtanφ’convention,whether linear or non-linear.

(12)Recently the ‘c then σtanφ’approach was adopted with a new twist:namely the estimation of c and φ from separates halves of the equation for Q.The cohesive component CC and the frictional component FC appear to have been hiding in the empirically based Q-formulation,since the addition of UCS:giving the form Qc=Qσc/100.Low CC requires more shotcrete,low FC requires more bolting.A semi-empirical origin is suggested,as Q-parameter ratings were adjusted in response to shotcrete and bolting needs described in the 200-plus 1974 case records.

(13)Numerical modelling with the discrete addition of rock joints in UDEC and 3DEC represents a big step in the direction of more realistic modelling of excavation effects in rock masses,for the purpose of deformation prediction and support design.(14)There is however a pitfall in distinct element(jointed)modelling because many modellers appear to exaggerate joint continuity.This is presumably done because it involves less work.It is more time-consuming to create models with more geologically realistic jointing of generally reduced continuity with depth,unless sedimentary rock remains at depth.

(15)Exaggerating joint continuity,especially in 2D UDEC models,may cause at least a ten-times exaggeration of deformation in comparison to measured results of e.g.cavern deformation response.It is wise to check numerical model predictions of displacement with empirical Q-based formulae,which are based on hundreds of measurements in tunnels and rock caverns.

(16)Stress transformation of principal stresses onto an inclined geologic plane or potential failure plane that dilates during shearing,has already violated three of the assumptions of the theory:the plane should be imaginary and it should not shear or dilate.

(17)Many geotechnical materials dilate during shear:non-planar rock joints,compacted rock fill,dense sand,over-consolidated clay.Large-scale experiments with biaxial testing of rock joints or fractures suggest the need to add a mobilized dilation angle into the stress transformation equations.Measured strength then corresponds to this modified stress transformation.

Acknowledgements

The author would like to thank the Editor for his expert assistance in the production of this paper.

3.引导学生掌握正确的学习方式。生物学科属自然科学，自然科学以实验为基础，特别是探究性实验。所以在初中生物学教学中要注意：一是教学要与生产生活实际相联系，粮食作物、蔬菜、瓜果、花卉等都是人类种植栽培的主要对象，在作物、花卉中有许多适合学生观察、探究的内容，教师应积极组织学生开展各种探究活动，加深学生对相关知识的理解，提高学生运用知识解决实际问题的能力；二是要积极开展实验教学，发挥实验设施设备在学生学习中的重要作用，让学生从观察、实验、讨论、探究的过程中获得对生物学知识的理解，亲身体验获取知识的过程和方法，才能加深学生对生物学中各知识点的理解与掌握。

Appendix A.

See Fig.A.1.

Fig.A.1.Shear strength description using Jr/Jafrom the Q-system(Barton et al.,1974;Barton,2002).

Bakhtar K,Barton N.Large scale static and dynamic friction experiments.In:Proceedings of the 25th US rock mechanics symposium.Illinois:Northwestern University;1984.p.139-70.

Barton N.A model study of the behaviour of steep excavated rock slopes.London:University of London;1971,PhD Thesis.

Barton N.Review of a new shear strength criterion for rock joints.Engineering Geology 1973;7(4):287-332.

Barton N,Lien R,Lunde J.Engineering classification of rock masses for the design of tunnel support.Rock Mechanics 1974;6(4):189-236.

Barton N.The shear strength of rock and rock joints.International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts 1976;13(9):255-79.

Barton N,Choubey V.The shear strength of rock joints in theory and practice.Rock Mechanics 1977;10(1/2):1-54.

Barton N,Kjærnsli B.Shear strength of rock fill.Journal of the Geotechnical Engineering Division 1981;107(GT7):873-91.

Barton N.Modelling rock joint behaviour from in situ block tests:implications for nuclear waste repository design.Office of Nuclear Waste Isolation ONWI-308:Columbus,OH;1982.p.96.

Barton N,Bandis S.Effects of block size on the shear behaviour of jointed rock.In:Keynote lecture.Proceedings of the 23rd US symposium on rock mechanics;1982.p.739-60.

Barton N,By TL,Chryssanthakis P,Tunbridge L,Kristiansen J,Løset F,Bhasin RK,Westerdahl H,Vik G.Predicted and measured performance of the 62 m span Norwegian Olympic Ice Hockey Cavern at Gjøvik.International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts 1994;31(6):617-41.

Barton N.Some new Q-value correlations to assist in site characterization and tunnel design.International Journal of Rock Mechanics and Mining Sciences 2002;39(2):185-216.

Barton N.Rock quality,seismic velocity,attenuation and anisotropy.UK&Netherlands:Taylor&Francis;2006,729.

Barton N.Thermal over-closure of joints and rock masses and implications for HLW repositories.In:Proc.of 11th ISRM congress;2007.p.109-16.

Barton N.From empiricism,through theory to problem solving in rock engineering.In:Qian QH,Zhou YX,editors.ISRM cong,6th Müller lecture.Proceedings,Harmonising rock engineering and the environment.Beijing:Taylor&Francis;2011.p.3-14.

Barton N,Pandey SK.Numerical modelling of two stoping methods in two Indian mines using degradation of c and mobilization of φ based on Q-parameters.International Journal of Rock Mechanics and Mining Sciences 2011;48(7),1095-1012.

Hajiabdolmajid V,Martin CD,Kaiser PK.Modelling brittle failure.In:Proc.4th North American rock mechanics symposium,NARMS 2000.A.A.Balkema;2000.p.991-8.

Müller L.The progressive failure in jointed media.In:Proc.of ISRM congress;1966.p.679-86[in German].

Singh M, Singh B. Modified Mohr-Coulomb criterion for non-linear triaxial and polyaxial strength of intact rocks.International Journal of Rock Mechanics and Mining Sciences 2011;48(4):546-55.

Singh M,Singh B.Modified Mohr-Coulomb criterion for non-linear triaxial and polyaxial strength of jointed rocks.International Journal of Rock Mechanics and Mining Sciences 2012;51(1):43-52.

Nick Barton has had a long-standing(45 years)interest in how rock joints and artificial fractures behave.These after all,are the remaining components of shear strength of a rock mass,after possible ‘intact bridges’have failed at smaller strains.This important reality-the influence of relative amounts of deformation,is ignored in M-C and H-B and GSI equations.

The author’s rock-joint related research at Imperial College,with parallel studies by student friends Peter Cundall and John Sharp,started exactly when the first ISRM congress had been held in Lisbon in 1966,where both Patton and Müller stimulated both conscious and subconscious contributions,both of which appear in the above article,and will be found with a little searching.