外文翻译-数值模拟中岩体力学特性的工程与实验关系

The Relation Between In situ and Laboratory RockProperties Used in Numerical ModellingINTRODUCTIONNumerical 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 propertiesused 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.METHODOLOGYThe 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 synthesizing 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.RESULTSFigure 1 presents the Youngs 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 the 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 Poisons ratio with no significant conclusions to be drawn.TECHNIQUES OF REDUCTIONA 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.（1） （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 Youngs modulus. （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. （4）Fig. 1. (a) Youngs modulus from case histories for laboratory tests and numerical modelling input (range 0-120 GPa). (b)Youngs modulus from cast histories for laboratory tests and numerical modelling input (range 0-28 GPa).Fig. 2. Youngs modulus from case histories for laboratory tests and numerical modelling input.Fig. 3. The relationship between laboratory Youngs modulus and the reduction factor used for numerical modelling.Fig. 4. (a) Uniaxial compressive strength from case histories for laboratory tests and numerical modelling input (range0-200 MPa). (b) Uniaxial compressive strength from case histories for laboratory tests and numerical modelling input (range0-40 MPa).Fig. 5. Uniaxial compressive strength from case histories for laboratory tests and numerical modelling input.Fig. 6. The relationship between laboratory uniaxial compressive strength and the reduction factor used for numerical modelling.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 ，actually measured around a roadway and the n displacements, obtained by a finite element analysis. Since the numerical model output depends on the values of elastic parameter E assumed in the finite element calculations, the error is in turn a function of these parameters (i.e.). Thus, the elements of vector E minimising 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. （5）Daniel 8, using a volumetric approach, reduced the laboratory-determined mechanical properties, rock stiffness 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). (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: （7）Cohesion of rock mass： (8)Friction angle of rock mass （9）Truemans 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: (10)where is the major principal stress, is the minor principal stress, is the uniaxial compressive strength of 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 determination of m and s for undisturbed and disturbed rock masses as follows:(1) For undisturbed rock masses： (11)where the value is a constant dependent upon the properties of the intact rock. (12)(2) For disturbed rock massesFig. 8. Poissons ratio from case histories for laboratory tests and numerical modelling input.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 thefollowing strength reductions based on his UK coal mining experience:RF= 1 for strong massive unjointed rock (including concrete)2 for widely spaced joints or bedding planes in strong rocks3 for more jointed but still massive rock4. for well jointed and weaker rock5 for unstable seatearths and closely cleated rock such as coal6or7 for weak rock in the neighbourhood of a fault zone.CONCLUSIONSThis 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 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 Browns 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.Fig. 9. 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