外文翻译-数值模拟中原位岩体与实验岩体的力学特性关系

翻译部分 外文原文：The Relation Between In situ and Laboratory Rock Properties Used in Numerical Modelling（N. MOHAMMAD，D. J. REDDISH，L. R. STACE）INTRODUCTIONNumerical 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.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）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 masses: (13) (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 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. 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.Fig. 8. Poissons ratio from case histories for laboratory tests and numerical modelling input.Fig. 9. Youngs modulus from case histories for laboratory tests and numerical modelling input.中文译文：数值模拟中原位岩体与实验岩体的力学特性关系1前言随着更便宜、高效的软件和硬件的应用，数值模拟正越来越多的应用于岩土工程设计。然而，数值模拟中关键的一步在于确定岩体的力学特性参数，即更精确的岩石硬度和强度特性。本文给出了一系列文章中用来岩体数值模拟的硬度与强度特性。给出实验和模型特性的文章都选自大量通用的模拟文献。具体来说，将所有从实验到现场使用简化强度和硬度参数的文献标记出来搜索，其结果令人吃惊：在数以千记的数值模拟文献，只有几百篇提到了实验岩体特性，而且在这些文章当中，只有40篇似乎使用了某种程度上的换算。那些使用换算参数的文章被做成曲线图构成了本文的主要内容。当岩石硬度特性与强度特性被分别分析时，它们各自的平均换算系数呈现出有趣的差异。2研究方法在审阅文献过程中，本文广泛的研究了不同岩石结构的各案例历史和数值模拟反演分析例。每一篇审阅过的文章都依据实验室测定岩石特性和数值模拟岩体输入特性以及其他相关的定量数据被收入数据库。大多数的文章都只提供了不完整数据，它们不是忽略了关键参数就是人为给出了参数，有些文章给出了实验岩体特性，只有很少数文章解释了根据岩体等级使实验岩体特性适应岩体的过程。人们只能认为这些特性的选取与该模型的来源或模型建立者有关，例如钢材从没有尺寸效应的环境中选取。几乎没有岩石力学专家拒绝承认即使是强度最大的岩石在其岩体特性上也需要调整，因此本文给出的图表和数据都集中在那些使用换算系数的文章上。一些具有最有效的相关数值的文章也在本文的结尾处给出。3研究结果图1为实验测出的杨氏模量与模型使用的杨氏模量的曲线。曲线中每个案例都根据其来源编号。如果将这些数据直线拟合可得到一个显著的趋势：模型使用的硬度平均是实验测出硬度的0.469倍（图2），类似的数据也可用换算系数绘出，如图3所示。在这里，低硬度岩石使用的换算系数有明显增高的趋势，在一些低硬度岩石中甚至可见到很高的换算系数。图4给出了实验测出的单轴压缩强度与模型使用的单轴压缩强度的曲线。曲线中每个案例都根据其来源编号。如果将这些数据直线拟合可得到一个显著的趋势：模型使用的强度平均是实验测出强度的0.284倍（图5），类似的数据也可用换算系数绘出，如图6所示。在这里，软弱岩石使用的换算系数也有明显增高的趋势。图7给出了抗拉强度的趋势表明实验值大至是由两个因素而减小的，图8则表明泊松比没有明显的下降趋势。4换算方法许多作者提出了一些实验室和现场之间的岩石特性关系，有些在关系中还包括了岩体分级。由Bieniawski提出的广泛应用的推导变形模量的公式1当RMR大于50时有18.2%的误差。然而，当RMR小于或等于50时，Bieniawski公式因会导致变形模量小于或等于0而变得不再适用。Serafim和 Pereira39使用 Bieniawski的岩体分级系统(RMR)得到了用于完整RMR变化的另一表达式，公式(2)： （1） （2）图9给出了根据硬度数据得出的所有绘图表达式。一个双向X轴被用来比较这些数据，这就要求RMR与实验弹性模量相关。一个简单的线性关系已经在所有典型特性中使用。（RMR = 0-100， E = 0-120 GPa.）Nicholson 和 Bieniawski 40，给出了一个换算因素的经验公式，公式（3）。这个因数被计算出来用以得到用来计算RMR和实验杨氏模量的岩体变形模量。 （3）Mitri et al. 33 使用下面的公式（4）来得到岩体的变形模量和计算出胡克-布朗参数来表现工程情况下的RMR： （4）被绘出（图9）的公式3和公式4采用以上相似的数据处理方法。当RMR低于30时，公式3可以用以硬度的大规模换算。公式4可能更适合于在低RMR和低硬度范围时的实际换算。尽管比较的公式曲线和数据是由简单的RMR和实验硬度线性关系组成的，但是仍然可以清楚的看出所有公式在低RMR范围时硬度都减少了很多。Matsui 9 提出了一个基于最小误差函数的直接方法，公式5。这个函数表示了n向位移（根据实际巷道围岩测量）和n向位移（由有限元分析获得）的最小二乘差换算。因为数值模型中输出的值是依据在有限元分析中假设的弹性模量参数值确定的，误差也是这些参数的函数（即）。因此，矢量弹性模量元素的减小代表了采用有限元模型方法对岩体的真实行为最好说明的弹性常量值。为了应用这种方法需要将弹性常量融入有限元程序。简单来说，很难将这种方法与其他方法比较。它实际上是一个对未知岩体特性的系统反分析方法。 (5)Daniel 8,使用了一种测定体积的方