翻译--The relation between in situ and laboratory rock properties used in numerical modelling.pdf

Pergamon Int J Rock Mech Min Sci Vol 34 No 2 pp 289 297 1997 1997 Elsevier Science Ltd Printed in Great Britain All rights reserved PII S0148 9062 96 00060 5 0148 9062 97 17 00 0 00 Technical Note The Relation Between In situ and Laboratory Rock Properties Used in Numerical Modelling N MOHAMMADt D J REDDISHt L R STACE t INTRODUCTION Numerical models are being used increasingly for rock mechanics design as cheaper and more efficient software and hardware become available However a crucial step in modelling is the determination of rock mass mechanical properties more precisely rock stiffness and strength properties This paper presents the results of a review of numerical modelling stiffness and strength properties used to simulate rock masses Papers where laboratory and modelling properties are given have been selected from the mass of more general modelling literature More specifically papers that have reduced stiffness and or strength parameters from laboratory to field values have been targeted The result of the search has been surprising of the thousands of papers on numerical modelling a few hundred mention laboratory and rock mass properties and of those only some 40 appear to apply some kind of reduction The papers that apply a reduction have been used to produce the graphs that constitute the main content of this paper Rock stiffness properties have been separated from those of strength in the analysis and this has illustrated interesting differences in their respective average reduction factors METHODOLOGY The review conducted has studied case histories and back analysis examples of numerical modelling for a wide range of rock structures Each reviewed paper has been databased in terms of laboratory measured rock properties and numerical modelling rock mass input properties plus other relevant quantitative data 1 37 The vast majority of papers have provided incomplete data either omitting key parameters or synthesising tDepartment of Mineral Resources Engineering University of Nottingham Nottingham NG7 2RD U K Author to whom correspondence should be addressed parameters Some papers have given laboratory and mass properties and a few papers have explained the process by which laboratory properties have been adjusted to the rock mass by use of rock mass ratings One can only conclude that this is related to the origin of the models or modellers being from environments where materials like steel have no scale effects There would be few rock mechanics specialists who would not acknowledge that even the strongest rock types need some adjustment of their rock mass properties The graphs and data provided in this paper have therefore concentrated on papers where reductions have been applied A list of the most valid and relevant numerical papers is included at the end of the paper RESULTS Figure 1 presents the Young s modulus results for laboratory tests plotted with those used in the model Each case is numbered against its source There is a simple trend in these data and if a straight line is fitted model stiffness is on average 0 469 of rthe laboratory stiffness Fig 2 The data can alternatively be plotted as reduction factors as in Fig 3 Here a trend of increased reduction factors for low stiffness rock types becomes apparent A number of very high reduction factors can also be seen for very low stiffness rocks Figure 4 shows the uniaxial compressive strength results for laboratory tests plotted against those used in the model Each case is numbered against its source There is a simple trend in these data and if a straight line is fitted model strength is on average 0 284 of the laboratory strength Fig 5 The data can alternatively be plotted as reduction factors as in Fig 6 Here a trend of increased reduction factors for weak rock types becomes apparent Figure 7 illustrates the trend for tensile strength indicating that the laboratory values are reduced by a factor of almost two and Fig 8 shows the trend for 289 290 MOHAMMAD et al TECHNICAL NOTE a ll0000 100000 800O0 60000 24 32 o 32 1 2121 o t Dr 0 2O00O 4O0OO 6O000 Laboratory E MPa b 2O0OO 4 14 14 30 30 2121 21 21 I 80OO0 27 30 16 21 i 10OOOO 120000 m I0000 5000 15 14 203 1 12 12 12 12 Oil 12 14 24 5 18 20 I S 1 o t i o 11 0 5000 10000 7 2 14 18 24 17 12 10 19 24 24 13 19 13 t 11 7 15000 2 100 25000 Laboratory E MdPa Fig 1 a Young s modulus from case histories for laboratory tests and numerical modelling input range 0 120 GPa b Young s modulus from cast histories for laboratory tests and numerical modelling input range 0 28 GPa MOHAMMAD et al TECHNICAL NOTE 291 120000 100000 y 0 4692x R 2 0 693 R z R squared valueaad is a measure of the data s fit to a line 80000 60000 4 I 40000 00 00 O0 20000 1 Q O v I I I I 0 20000 40000 60000 80000 100000 Laboratory g MPa Fig 2 Young s modulus from case histories for laboratory tests and numerical modelling input 120000 Poissons ratio with no significant conclusions to be drawn TECHNIQUES OF REDUCTION A number of authors have presented relations between laboratory and in situ properties Some have included rock mass ratings in their relations The widely used technique to derive deformation moduli is equation 1 presented by Bieniawski 38 for rocks having a Rock Mass Rating RMR greater than 50 with a prediction error of 18 2 However when the RMR is less than or equal to 50 the Bieniawski formula is not applicable as it leads to values of deformation moduli less than or equal to zero Serafim and Pereira 39 using the Bieniawski Rock Mass Classification system RMR derived an alternative expression equation 2 for the entire range of RMR Em 2RMR 100 GPa 1 45 40 O y 5 1801e lE OSx K a ffi 0 0754 35 30 10 5 0 Q 00 O0 0 I I I I 0 20000 40000 60000 80000 100000 Laboratory g MPa Fig 3 The relationship between laboratory Young s modulus and the reduction factor used for numerical modelling 120000 292 MOHAMMAD et al TECHNICAL NOTE a 60 i 40 20 24 O 24 24 24 r J 20 40 b 24 24 24 24 24 32 32 34 37 34 r3 35 1 1 lq l l h k oO 1919 23 32 36 3619 O0 12 28 37 I I 20 14 I I 60 80 100 120 140 160 180 200 Laboratory UCS MPa 10 4 24 9 34 23 35 10 1 O I 10 10 10814 13 12e 35 13 35 36 13 12 13 r I I I I I 5 10 15 20 25 30 35 l boratory UCS MPa Fig 4 a Uniaxial compressive strength from case histories for laboratory tests and numerical modelling input range 0 200 MPa b Uniaxial compressive strength from case histories for laboratory tests and numerical modelling input range 0 40 MPa 40 MOHAMMAD et al TECHNICAL NOTE 293 140 120 100 40 2O 0 y 0 2837x R 2 0 2718 20 40 60 80 1 120 1 Laboratory UCS MPa Fig 5 Uniaxial compressive strength from case histories for laboratory tests and numerical modelling input RMR 10 gm 10 00 aPa 2 Figure 9 shows both the expressions plotted against the stiffness data from the review A double x axis has been used to compare these data This has required the RMR to be related to laboratory E A simple linear relation has been used over the typical full of both properties RMR 0 100 and E 0 120 GPa Nicholson and Bieniawski 40 have developed an empirical expression for a reduction factor equation 3 This factor is calculated in order to derive deformation moduli for a rock mass using its RMR and a laboratory Young s modulus RMR RF Ei E 0 0028RMR2 0 9 exp 22 Z f 3 Mitri et al 33 used the following equation 4 to derive the modulus of deformation of the rock mass and scaled down the Hoek Brown parameters to represent an in situ situation using the RMR RF E I RMR Ein 0 5 I coskn li 0 0 J j 4 20 18 16 14 n I 10 mN I s 6 Up nun i n iiln g i 2 i I 0 I I J I r y 5 3466e o 01Mx R 2 0 3383 0 70 40 60 80 100 120 140 Laboratory UCS Ilia Fig 6 The relationship between laboratory uniaxial compressive strength and the reduction factor used for numerical modelling 294 MOHAMMAD et al TECHNICAL NOTE 18 16 14 12 g 6 4 2 0 y 0 4943x R 0 s 3 I i 5 10 15 20 Laboratory UTS MPa 25 Fig 7 Uniaxial tensile strength from case histories for laboratory tests and numerical modelling input Equations 3 and 4 have been plotted Fig 9 in a similar way to the above data Equation 3 can be seen to apply large reductions to the stiffness once the RMR is below 30 Equation 4 is a much better fit to the data and has perhaps more realistic reductions in the low RMR and stiffness range Although comparisons between the equation lines and the data are composed by the simple linear relation being used between the RMR and laboratory stiffness it is still clear that both formulae reduce stiffness too much in the low RMR range Matsui 9 presented a direct approach based on the minimisation of an error function equation 5 This function represents a least squares reduction of discrepancy between the n displacements uj actually measured around a roadway and the n displacements u obtained by a finite element analysis Since the numerical model output uP depends on the values of elastic parameter E assumed in the finite element calculations the error E is in turn a function of these parameters i e E fIE Thus the elements of vector E minimising E represent the values of the elastic constants which lead to the best description of the behaviour of the real rock mass by means of the finite element model To use this approach it is necessary to integrate it into the finite element package It is therefore difficult to compare in simple terms with other approaches It is in effect a systematic back analysis approach where the unknown is the rock mass property 1 Daniel 8 using a volumetric approach reduced the laboratory determined mechanical properties rock stiff ness and strength by a scale factor of 1 6 for input into the model This was to account for discontinuities and pore water pressure which depend on the size of the element representing the rock The reduction factor was estimated according to formula 6 RF V0 6 where V0 is the volume of the rock used in the laboratory testing and V is the volume of the rock used in the finite element model Trueman 12 after reviewing different reduction factors proposed by others derived the RMR based expressions for reduced strength parameters Uniaxial compressive strength of rock mass ann 0 5 exp 0 06 RMR MPa 7 Cohesion of rock mass C m 0 25 exp 0 05 RMR MPa 8 Friction angle of rock mass q m 0 5 RMR 5 degrees 9 Trueman s technique has been used by different authors 14 23 41 who found it successful in their respective numerical studies Hoek and Brown 42 developed a criterion that could be used to take into account the overall condition of the rock mass This criterion allows for the intact rock response influence of joints and behaviour of discontinuities in the rock mass 0 1 0 3 m0 30 so 2 10 where 0 1 is the major principal stress 0 3 is the minor principal stress ac is the uniaxial compressive strength of 0 5 Y 0 45 R 2 0 2642 4 0 4 4 4 4 4 0 35 4 0 3 L 4 A4 0 2 0 15 a t 4 0 0 4 0 0 l 1 I 0 0 I 0 2 0 3 0 4 0 5 Laboratory Po ssons Ratio Fig 8 Poisson s ratio from case histories for laboratory tests and numerical modelling input MOHAMMAD et al TECHNICAL NOTE 295 120000 100000 80000 60000 40000 20000 16 33 t I 1 Y 0 4692X R 2 0 693 RMR 50 66 83 I 3 E 2RMR 100 lo 4 E 10 5 RF Ei tE O 0 0 2 8 R M R Z 0 9exp 2 t z R MR 2 oO 20000 40000 60000 0000 100000 Laboratory E MPa Fig 9 Young s modulus from case histories for laboratory tests and numerical modelling input 100 120000 the rock and m and s are the constants dependent upon the properties of the rock Hock and Brown 43 updated their equation 10 on the basis of the Bieniawski rock mass classification RMR and presented new expressions for the determi nation of m and s for undisturbed and disturbed rock masses as follows 1 For undisturbed rock masses I RMR 28 100 m mi exp 11 where the rn value is a constant dependent upon the properties of the intact rock s exp 2 For disturbed rock masses fRMR 100 m m exp 13 s exp RMR 100 14 This approach is probably the most advanced to date as it allows for the effect of rock mass on the whole failure envelope and is therefore somewhat more sophisticated than the earlier simple reduction factors Wilson 44 based on published work suggested that with a closely cleated rock the strength varies approximately as the inverse of the cube root of the specimen dimension Comparing laboratory specimen size to roadway size this implies that for such a rock the laboratory strength should typically be divided by five in order to obtain arm In a massive rock with widely spaced joints the dividing factor will probably remain at unity until the specimen size is greater than the joint spacing On the other hand in a highly faulted area the dividing factor could well exceed five Wilson proposed the following strength reductions based on his UK coal mining experience RF 1 2 6or7 for strong massive unjointed rock in cluding concrete for widely spaced joints or bedding planes in strong rocks for more jointed but still massive rock for well jointed and weaker rock for unstable seatearths and closely cleated rock such as coal for weak rock in the neighbourhood of a fault zone CONCLUSIONS This paper has examined reduction factor applied to rock properties found from laboratory testing in order for the data to be applied in numerical modelling The data used have been extracted from 44 separate 296 MOHAMMAD et al TECHNICAL NOTE published works It was found that strength and stiffness properties needed to be treated separately when examining the effect of the rock mass upon them In the simplest terms strength on average was reduced by around a quarter and stiffness by around a half Of the expressions evaluated equation 4 would appear to be the best in predicting stiffness properties although below RMRs of 20 its reduction would appear excessive Strength is best modelled either by the Trueman approach equations 7 9 for a simple Molar Coulomb model or by Hoek and Brown s more complex approach for a better failure envelope equations 10 14 However it was found that in the case of low strength stiffness or RMR the above approaches may prove unsatisfactory Further research into the relations for these weak types of rocks continues As a final word of caution in the analysis of the values from the review the modelled rock mass property values are not necessarily measured or back analysis derived but are in some cases simply the opinion of the particular engineer Because of this a bias towards accepted practice or opinion could well be present in the distribution of results Accepted for publication 14 October 1996 REFERENCES 1 Bardet J and Scott R F Seismic stability of fractured rock using distinct element method Proceedings of the 26th US Symposium on Rock Mechanics ed Eileen Ashworth 1985 pp 139 149 2 Adams D J Gurtunca R G Jager A J and Gay N C Assessment of a new mine layout incorporating concrete pillars as regional support In Innovation in Mining Backfill Technology Balkema Rotterdam 1989 pp 199 208 3 Yao X L Reddish D J and Whittaker B N Non linear finite element analysis of surface 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