测线取样法引起的岩体结构面几何偏差纠正

发布时间：2018-01-14 04:17

本文关键词：测线取样法引起的岩体结构面几何偏差纠正　出处：《中国地质大学》2014年博士论文　论文类型：学位论文

【摘要】：重要工程构筑物的建造和运行例如公路、隧道、坝基、港口地基、桥基、高楼大多涉及到岩体。理想人造材料是连续和均匀的介质,而岩体是一个复杂的、经历了长期有些是上千亿年的物理地质和工程地质作用的地质体,因此岩体形成各种不均匀和不连续的结构,岩体结构主要由完整岩块和结构面两个部分组成。结构面定义为包含各种地质成因的不连续面,它包括层面、断层、裂隙、裂纹、节理和其它相对于周围岩石具有一些共同的特征如较低的剪切强度、微小的抗拉强度和较好的流体渗透性的力学缺陷。大量的工程实例证明结构面的几何特征很大程度上控制了工程岩体的力学性能如变形模式和稳定性。结构面的几何特征通常采用窗取样法和线取样法两种取样技术获得。本文只考虑线取样法,它包括钻孔法和测线法,集中研究测线法。测线法是统计与测线相交的结构面,而不相交的结构面则不统计,该方法被广泛使用在露头面上,尽量选择一个清晰、平坦的、相对于结构面尺寸和间距更大的岩石面,出露点一般分布于海滩陡岸、峡谷、路堑、矿场和露天矿山等,在选取测量面时应保证测量面岩体和结构面能够代表该场地的整个特征。很多自然的和开挖的岩体表面由节理面和断层面组成,当这些面被选为测量面时,此时有必要布置多条不同方位的测线进行测量,以便于全面统计三维空间内结构面网络。测线法不可避免的存在产状取样偏差,即测线优先交切与它交角比较大的结构面。Terzaghi在1965年首次对此偏差进行纠正,她用产状观测频率除以交角的正弦来获取纠正后的频率。这种方法自从提出,已经被广泛运用。 Terzaghi方法应用在盲区内(与测线交角小于30°)时是无效的。1.前人提出了大量避免盲区的方法,然而,盲区以外(与测线交角大于30°)的纠偏效果却很少被注意。目前为止,盲区以外的低效来源仍然是未知,同时提高盲区以外效果的方法也未见。2.网格化投影图是Terzaghi方法的内部步骤之一,它一直被前人所使用,以致于人们习惯认为网格化是Terzaghi方法的必要步骤之一。其实,目前为止,网格化的必要性还有待检验,网格化是否会给纠编结果带来误差还有待研究。3.Tang在2013年最新的研究指出,即使采用优化措施,Terzaghi方法纠偏结果仍然具有很高的误差。目前缺乏高效的纠偏方法。本文研究主要包含三个部分：1.寻找Terzaghi方法应用于盲区外时纠偏低效来源,给出提高纠偏效果的建议。2.对于Terzaghi的方法,评估网格化的必要性。如果评估结果显示网格化是不必要的,测试非网格化代替网格化的可行性,并对这两种情况下得到的纠偏结果进行效果比较。3.基于产状在三维空间内的概率分布解,提出一种比Terzaghi方法更有效的纠偏方法。这三个方面的研究方法分别是： 1.我们怀疑低效来自于Terzaghi公式。因此为探索来源,我们需要Terzaghi公式的整个推导过程。鉴于Terzaghi在1965年给出的推导较为简单,我们利用解析几何学、概率论和积分学的方法作出了更为详细和合理的推导过程。我们试图在推导中找到可能带来误差的步骤。为提高效果,我们给出两个参数(网格大小和样本密度)的建议值。网格大小是Terzaghi方法中的一个设定参数,采样密度是样本数除以倾向的上下限之差、再除以倾角的上下限之差后的一个参数。 (1)通过试验测得这两个参数一系列组合的效果大小。 (2)将具有最高效果的一对参数选为建议值。 (3)采用四川省汶川地区实测的长石砂岩结构面产状数据验证网格大小建议值和样本密度建议值的合理性。第一,用测线法实测获取倾向和倾角数据；第二,用Terzaghi方法纠偏实测数据；第三,采用纠偏后数据,建立结构面的随机三维网络模型。在该模型中,利用与野外实测测线产状一致的虚拟测线获取与之相交结构面的倾向和倾角。为区分野外实测产状,我们将从模型中获取的产状命名为“模型产状”；第四,利用Kolmogorov-Smimov双样本检验法,测试不同网格大小下实测产状与模型产状的概率分布差异。 2.评价无网格化时的误差量级。 (1)有必要测试无网格化的可行性。 (2)基于前述的实测产状数据比较网格化与不网格化的误差。利用纠偏结果构建结构面三维网络模型,从模型中得到55个测量产状数据,用Kolmogorov-Smimov双样本检验法测试了原始产状概率分布和模拟产状概率分布之间的误差。另一方面,利用结构面随机网络模拟开展精度测试,此模拟与实测数据相比拥有更多测线产状和样本数的组合。第一,建立结构面、露头和测线模型,并且获取与测线相交的结构面产状。为区分这些相交的产状,岩体三维空间内的产状被称为“原始产状”。然后,利用Terzaghi方法,分别在网格化和非网格化的两种情况下对获取的产状数据进行频率纠偏。紧接着,用Kolmogorov-Smimov双样本检验法测试原始产状和纠偏后产状之间的概率分布差异。 (3)比较网格化与非网格化两种情况下概率分布差异大小,如果非网格化差异较小,则讨论非网格化代替网格化的可行性。 3.提出一种更更有效的纠偏方法。 (1)用积分方法推导产状的概率密度函数(为数值解)。 (2)然后在此函数基础上提出了包括2个假设和5个步骤的数值解法。两个假设是： (a)假设每一分组内的产状概率分布与直径概率分布是相互独立的； (b)假设在岩体三维空间中,每一分组内的两个产状元素(倾向和倾角)概率分布是相互独立的。同样的假设也应适用于与测线或钻孔相交的结构面产状。五个步骤包括： (a)分组。可利用Dips软件实现。需注意的是每个分组都应各自进行分析和纠偏。 (b)检验倾向与倾角之间的独立性。由前面假设可知倾向与倾角之间须保持独立,因此有必要检验实测产状的倾向与倾角是否满足这个假设。独立性测试方法有许多种,Pearson开方(x2)检验法就是其中之一。 (c)根据推导的数值解纠正倾向与倾角的概率分布。 (d)判断纠偏后的产状概率分布类型。 (e)计算修正后的产状分布参数。此处参数选择需先考虑概率分布类型,已经由步骤4确定。例如,对于正态分布,参数为均值和标准差(或方差)；对于对数正态分布,参数为均值和对数标准差(或方差)；对于均匀分布,参数为下限和上限；对于指数分布,参数为均值。确定好参数形式后,可以利用Matlab或SPSS通过最小二乘法得到参数值。对于步骤4,在一般的统计分析中,有两种用于判断概率分布类型的方式：从概率密度曲线形状判断或从累积分布曲线形状判断。为了在两种方式之间选取较合适者,在4种产状分布类型下比较两种方式有效性。比较的程序如下： (a)不妨假定产状和其他为建模所必需的参数(如大小、密度、张开度)。其中假设的产状分布包括4种类型,分别为正态分布,对数正态分布,均匀分布和指数分布；为每种分布类型设定7种样本数,分别为50,100,150,200,300,500和1000。 (b)输入这些参数,采用随机模拟方法建立结构面的三维网络模型。根据4种不同的概率分布,建立4个不同的结构面网络模型。 (c)获取模型中与测线相交的结构面的产状数据。针对每种模型,采用7种不同的样本数进行测量。因此,对于4中模型,共得到28个系列的产状数据。 (d)由于提出的方法是基于实测倾向和倾角之间独立性假设,因此,在纠偏前就得采用Pearson开方(x2)检验法测试此独立性。 (e)为得到概率密度曲线,纠偏28个产状系列；为得到累积分布曲线,也纠偏这些系列。然后对比两者的有效性。 (3)利用前述实测产状数据比较提出方法与Terzaghi方法的纠偏效果。研究得到如下结论： 1.更详细、合理地推导了Terzaghi的纠偏公式。推导过程中发现,在盲区以外,Terzaghi方法由于公式中的近似替代而产生理论误差。因此,为了提高纠偏效果,通过试验和实例验证给出了网格大小和样本密度的建议值,即网格大小为2°×2°以及样本密度为0.05°-2时误差最小。 2.作为Terzaghi的方法一个内部步骤,网格化投影图往往会给纠偏结果引入一个相当大的误差。试验证明非网格化是可行的。最后,网格化与非网格化的纠偏结果准确性比较表明,纠偏结果在无网格化的情况下比在网格化时更精确。 3.在推导产状在三维空间的概率分布函数的过程中,发现很难求取其解析解。所以推导出了数值近似解。基于数值近似解,提出了包含两个假设和五个步骤的产状纠偏的数值解方法。 4.对于提出的方法,概率密度曲线和累积分布曲线的判断分布类型效果对比显示,根据概率密度曲线很难清楚地判断产状分布类型,相反地,可以很容易地从累积分布曲线中看出。这表明,在分布类型的判断上,累积分布曲线比概率密度曲线更有效。所以相比于概率密度曲线和它的函数(概率密度函数),累积分布曲线和它的函数(累积分布函数)是最佳分布形式判断方式。 5.对于提出的方法,在各种样本数下的纠偏效果对比试验表明：(1)当倾向或倾角服从指数分布时,该方法是低效的。这说明该方法不适合指数分布的产状。(2)当倾向或倾角服从均匀分布时该方法是相当有效的。且增加样本数量几乎不影响其效果。表明该方法适合均匀分布的产状。(3)当产状服从正态分布且样本数量超过500,增加样品数很难提高效果。所以应该限制样本数量使其低于500。(4)当倾向或倾角服从对数正态分布且样本数量超过150时,增加样品数不能显著提高效果。所以150为对数正态分布最佳的样本数量。由于在测量和纠偏前未知分布类型,最佳样本数量的判断可能是上述四个情况之一。因此,结合上述四种结果后,为保证提出的方法高效性,最佳样本数量应约为150。 6.与Terzaghi方法相比,提出的方法更有效。原因可能是Terzaghi方法是假设在每个计数圆里的所有结构面是平行的。然而事实上,并不是所有的结构面都是平行的。这种假设与事实的不符造成了Terzaghi方法低效。而提出的方法不基于这个假设,所以其纠偏效果会更高。
[Abstract]:Important engineering structures such as the construction and operation of highway, tunnel, dam, bridge, port foundation, high-rise buildings are mostly related to the rock mass. The ideal artificial material is continuous and homogeneous medium, and the rock mass is a complex, after a long period of some geological bodies of hundreds of billions of years of physical and engineering geological effect, therefore the rock formation structure of various inhomogeneous and discontinuous rock mass structure, mainly composed of two parts of intact rock and surface structure. The structure surface is defined as a discontinuity contains various geological origin, including level, faults, fissures, cracks, joints and other relative to the surrounding rock has some common features such as shear strength low tensile strength, small and good fluid mechanics defects. A large number of engineering examples show that the characteristics of mechanical properties of geometric structure of the largely controlled rock mass such as variable Shape pattern and stability. The geometric features of the structural plane are usually obtained by two sampling techniques: the window sampling method and the line sampling method.
This paper only consider the line sampling method, it includes drilling method and line method, focus on the line. The line line intersection method is statistical and structural plane, and the structure is not disjoint surface statistics, this method is widely used in the outcrop on the surface, try to choose a clear, smooth. Compared to the larger rock surface structure surface size and spacing, the dew point generally distributed in the steep Shore Beach, canyon, cutting, mines and opencast mines, in the choice of measuring surface should guarantee the measurement of the surface of rock and structural plane can represent the entire site features. Many natural and rock excavation surface composed of joint the surface and fault surface, when the surface is selected as the measurement of the surface, it is necessary to arrange lines and a plurality of different range of measurement, in order to facilitate the comprehensive statistics in the three-dimensional space structure network.
There is the occurrence of sampling bias line method.Terzaghi is inevitable, structural plane line priority intersection with its relatively large angle for the first time in 1965 to correct this deviation, she uses sine attitude angle to obtain the observed frequency divided by the corrected frequency. Since this method is proposed, which has been widely used.
The application of Terzaghi method in the blind spot (and line angle less than 30 degrees) is invalid.1. predecessors put forward a lot of methods to avoid blind spots, however, blind outside (with line angle greater than 30 DEG) of the rectifying effect has rarely been noticed. So far, inefficient sources outside the blind area is still unknown, at the same time improve the method is not blind outside the effect of grid.2. projection is one of the internal procedure of Terzaghi method, it has been used by the predecessors, people used to think that the grid is one of the necessary steps of Terzaghi method. In fact, so far, the necessity of grid has yet to be tested, the grid will give the correction results error.3.Tang remains to be studied in the latest research in 2013 pointed out that even if the optimization measures, the Terzaghi method still has a very high error correction results. At present, the lack of efficient and correct recipe method.
This paper mainly includes three parts: 1. for Terzaghi method is applied to the blind spot when correcting inefficient sources, suggestions are given to improve the correction effect of.2. for Terzaghi, the need to evaluate the grid. If the assessment results show that the grid is not necessary, feasibility testing of non grid instead of the grid, and the rectification the results of the two cases were based on the effect of the.3. occurrence probability in three-dimensional space distribution solution, puts forward the correction a more effective method than the Terzaghi method.
The research methods of these three aspects are as follows:
1. we suspect that the inefficient from Terzaghi formula. So as to explore the source of the whole process, we need to derive Terzaghi formula. Given the derivation given by Terzaghi in 1965 is relatively simple, we use the method of analytic geometry, probability theory and integral theory gives a more detailed derivation and reasonable. We try to find possible error steps in the derivation. In order to improve the effect, we give two parameters (mesh size and sample density) recommended value. The size of the grid is a set of parameters in Terzaghi method, the sampling density is poor minimum sample number divided by the tendency, then a parameter difference limit by dividing the Inclination after.
(1) the effect of a series of combination of the two parameters is measured by the test.
(2) a pair of parameters which have the highest effect is selected as the recommended value.
(3) measured by the Sichuan area of Wenchuan Province, the rationality of the feldspar sandstone structure surface mesh size verification proposed like data values and sample density value. First, with the data line method and angle of the measured inclination; second, using the method of Terzaghi correction of measured data; third, the correction data, establish the 3D random structure network model. In this model, the field line with the same occurrence of virtual line gets the intersection with structural plane orientation and inclination. In order to distinguish the field occurrence, we will obtain from the occurrence model named "model of occurrence"; fourth, the use of Kolmogorov-Smimov two sample test method the probability distribution, difference test under different grid size measured occurrence and occurrence model.
2. evaluate the magnitude of error in meshless.
(1) it is necessary to test the feasibility of meshless.
(2) the actual occurrence data comparison and grid grid based on the error. The results to construct the three-dimensional network model by using the correction, 55 measurement occurrence data from the model, the error between the original occurrence probability distribution and simulate the occurrence probability distribution test Kolmogorov-Smimov two sample test method on the other hand, the use of structural plane network stochastic simulation to carry out precision test, the simulated and measured data compared with more test combination line occurrence and the number of samples. First, the establishment of structural surface, outcrop and line model, and obtain the structure and measuring line intersecting plane. To distinguish these intersect occurrence in three-dimensional space, rock occurrence is known as the "original form". Then, using the Terzaghi method, two cases were in the grid and non grid under the frequency correction of occurrence data obtained. Then, using Kolmogoro The v-Smimov double sample test was used to test the difference in the probability distribution between the original and rectifying production.
(3) we compare the difference of probability distribution between two cases of grid and non gridding. If the difference of non gridding is small, we discuss the feasibility of gridding instead of grid.
3. a more effective correction method is proposed.
(1) an integral method is used to deduce the probability density function (the numerical solution) of the yield.
(2) then a numerical solution of 2 hypotheses and 5 steps is proposed on the basis of this function.
The two hypothesis is:
(a) assuming that the probability distribution of the yield in each group is independent of the probability distribution of the diameter.
(b) suppose that in the three dimensional space of rock mass, the probability distribution of two occurrence elements (inclination and dip angle) in each group is independent. The same assumption should also apply to the occurrence of structural planes intersecting line or borehole.
The five steps include:
(a) groups. Can be implemented using Dips software. It is important to note that each group should be analyzed and rectified separately.
(b) the independence test between dip and dip angle. By assuming independence between the front to dip and dip angle, so it is necessary to test whether the tendency and inclination of measured shape satisfy this assumption. There are many kinds of independent test methods, Pearson extraction (x2) method is one of them.
(c) the probability distribution of the inclination and inclination is corrected by the derived numerical solution.
(d) to determine the type of probability distribution after correction.
(E) calculation of occurrence, the corrected parameters. This parameter selection should first consider the types of probability distribution has been determined by 4 steps. For example, the normal distribution parameters for the mean and standard deviation (or variance); for the lognormal distribution, the parameter as the mean and the logarithmic standard deviation (or variance); for the uniform distribution of parameters for the lower and upper bounds for the exponential distribution parameter; mean. Determine the parameter form, you can use the Matlab or SPSS by the least squares method to get parameter values.
In step 4, the statistical analysis in general, there are two types of probability distribution used to judge the way: the probability density curve of judgment or from the cumulative distribution curve shape. In order to judge between the two ways to select a suitable, effective comparison of two ways in 4 distribution types. The comparison the procedure is as follows:
(a) assume the occurrence and other necessary for modeling parameters (such as size, density, Zhang Kaidu). The hypothesis of occurrence, including 4 types, respectively, normal distribution, lognormal distribution, uniform distribution and exponential distribution; 7 of the sample number for each type of distribution. 50100150200300500 and 1000. respectively.
(b) input these parameters, and establish the 3D network model of the structural plane by using the stochastic simulation method. According to 4 different probability distributions, 4 different structural plane network models are established.
(c) get the occurrence data of the structural plane intersected with the survey line in the model. For each model, 7 different sample numbers are used for the measurement. Therefore, for the 4 models, 28 series of occurrence data are obtained.
(d) the proposed method is the assumption of independence, between the measured inclination and angle based on the result, should be adopted in the rectification before prescribing Pearson (x2) test method to test the independence.
(E) to get the probability density curve, rectify the 28 production series; to get the cumulative distribution curve, it also rectify these series, and then compare the effectiveness of the two.
(3) to compare the correction effect between the method and the Terzaghi method by comparing the previous measured data.
The conclusions are as follows:
1. more detailed, reasonable to deduce the correction formula of Terzaghi. It is found that the derivation process, in the area outside, Terzaghi method produced theoretical error due to approximate substitution in the formula. Therefore, in order to improve the rectification effect, through the test and verification of the grid size and density of the sample values suggested that grid size is 2 * 2 DEG and the sample density is 0.05 ~ -2 minimum error.
2. Terzaghi as a method of internal procedures, grid projection will often give a correction result to introduce a considerable error. Experimental results show that the non grid is feasible. Finally, the correction grid and non grid compared the accuracy of correction results in no grid than in the case of the grid more accurate.
3., in the process of deriving the probability distribution function of occurrence in three-dimensional space, it is difficult to obtain its analytical solution. Therefore, a numerical approximate solution is derived. Based on the approximate solution, a numerical solution method with two assumptions and five steps is proposed.
4. for the proposed method, show the probability density curve and cumulative distribution curve to determine distribution type contrast effect, according to the probability density curve is difficult to clearly determine the occurrence, types, on the contrary, can be easily seen from the cumulative distribution curve. This shows that the distribution patterns of judgment, the cumulative distribution curve is more effective than the probability density curve. Compared to the probability density function curve and its function (probability density function), and its cumulative distribution curve (cumulative distribution function) is the best way to determine the form distribution.
5. for the proposed method show that the rectifying effect contrast test in sample number: (1) when the tendency or inclination of exponential distribution, this method is inefficient. This shows that this method is not suitable for the occurrence of the exponential distribution. (2) when the tendency or inclination of uniform distribution when the method is quite effective. And increase the sample number almost does not affect the results. Show that the method is suitable for uniform occurrence. (3) when the number of occurrences obey normal distribution and sample of more than 500, increasing the number of samples is very difficult to improve the effect. We should limit the number of samples is less than 500. (4) when the tendency or inclination to obey the number of lognormal distribution and sample of more than 150, increasing the number of samples can significantly improve the effectiveness of

【学位授予单位】：中国地质大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TU45

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