本文關(guān)鍵詞：測線取樣法引起的巖體結(jié)構(gòu)面幾何偏差糾正　出處：《中國地質(zhì)大學》2014年博士論文　論文類型：學位論文

  更多相關(guān)文章： 巖體 結(jié)構(gòu)面 測線法 幾何偏差 糾正

【摘要】：重要工程構(gòu)筑物的建造和運行例如公路、隧道、壩基、港口地基、橋基、高樓大多涉及到巖體。理想人造材料是連續(xù)和均勻的介質(zhì),而巖體是一個復雜的、經(jīng)歷了長期有些是上千億年的物理地質(zhì)和工程地質(zhì)作用的地質(zhì)體,因此巖體形成各種不均勻和不連續(xù)的結(jié)構(gòu),巖體結(jié)構(gòu)主要由完整巖塊和結(jié)構(gòu)面兩個部分組成。結(jié)構(gòu)面定義為包含各種地質(zhì)成因的不連續(xù)面,它包括層面、斷層、裂隙、裂紋、節(jié)理和其它相對于周圍巖石具有一些共同的特征如較低的剪切強度、微小的抗拉強度和較好的流體滲透性的力學缺陷。大量的工程實例證明結(jié)構(gòu)面的幾何特征很大程度上控制了工程巖體的力學性能如變形模式和穩(wěn)定性。結(jié)構(gòu)面的幾何特征通常采用窗取樣法和線取樣法兩種取樣技術(shù)獲得。 本文只考慮線取樣法,它包括鉆孔法和測線法,集中研究測線法。測線法是統(tǒng)計與測線相交的結(jié)構(gòu)面,而不相交的結(jié)構(gòu)面則不統(tǒng)計,該方法被廣泛使用在露頭面上,盡量選擇一個清晰、平坦的、相對于結(jié)構(gòu)面尺寸和間距更大的巖石面,出露點一般分布于海灘陡岸、峽谷、路塹、礦場和露天礦山等,在選取測量面時應保證測量面巖體和結(jié)構(gòu)面能夠代表該場地的整個特征。很多自然的和開挖的巖體表面由節(jié)理面和斷層面組成,當這些面被選為測量面時,此時有必要布置多條不同方位的測線進行測量,以便于全面統(tǒng)計三維空間內(nèi)結(jié)構(gòu)面網(wǎng)絡。 測線法不可避免的存在產(chǎn)狀取樣偏差,即測線優(yōu)先交切與它交角比較大的結(jié)構(gòu)面。Terzaghi在1965年首次對此偏差進行糾正,她用產(chǎn)狀觀測頻率除以交角的正弦來獲取糾正后的頻率。這種方法自從提出,已經(jīng)被廣泛運用。 Terzaghi方法應用在盲區(qū)內(nèi)(與測線交角小于30°)時是無效的。1.前人提出了大量避免盲區(qū)的方法,然而,盲區(qū)以外(與測線交角大于30°)的糾偏效果卻很少被注意。目前為止,盲區(qū)以外的低效來源仍然是未知,同時提高盲區(qū)以外效果的方法也未見。2.網(wǎng)格化投影圖是Terzaghi方法的內(nèi)部步驟之一,它一直被前人所使用,以致于人們習慣認為網(wǎng)格化是Terzaghi方法的必要步驟之一。其實,目前為止,網(wǎng)格化的必要性還有待檢驗,網(wǎng)格化是否會給糾編結(jié)果帶來誤差還有待研究。3.Tang在2013年最新的研究指出,即使采用優(yōu)化措施,Terzaghi方法糾偏結(jié)果仍然具有很高的誤差。目前缺乏高效的糾偏方法。 本文研究主要包含三個部分：1.尋找Terzaghi方法應用于盲區(qū)外時糾偏低效來源,給出提高糾偏效果的建議。2.對于Terzaghi的方法,評估網(wǎng)格化的必要性。如果評估結(jié)果顯示網(wǎng)格化是不必要的,測試非網(wǎng)格化代替網(wǎng)格化的可行性,并對這兩種情況下得到的糾偏結(jié)果進行效果比較。3.基于產(chǎn)狀在三維空間內(nèi)的概率分布解,提出一種比Terzaghi方法更有效的糾偏方法。 這三個方面的研究方法分別是： 1.我們懷疑低效來自于Terzaghi公式。因此為探索來源,我們需要Terzaghi公式的整個推導過程。鑒于Terzaghi在1965年給出的推導較為簡單,我們利用解析幾何學、概率論和積分學的方法作出了更為詳細和合理的推導過程。我們試圖在推導中找到可能帶來誤差的步驟。為提高效果,我們給出兩個參數(shù)(網(wǎng)格大小和樣本密度)的建議值。網(wǎng)格大小是Terzaghi方法中的一個設定參數(shù),采樣密度是樣本數(shù)除以傾向的上下限之差、再除以傾角的上下限之差后的一個參數(shù)。 (1)通過試驗測得這兩個參數(shù)一系列組合的效果大小。 (2)將具有最高效果的一對參數(shù)選為建議值。 (3)采用四川省汶川地區(qū)實測的長石砂巖結(jié)構(gòu)面產(chǎn)狀數(shù)據(jù)驗證網(wǎng)格大小建議值和樣本密度建議值的合理性。第一,用測線法實測獲取傾向和傾角數(shù)據(jù)；第二,用Terzaghi方法糾偏實測數(shù)據(jù)；第三,采用糾偏后數(shù)據(jù),建立結(jié)構(gòu)面的隨機三維網(wǎng)絡模型。在該模型中,利用與野外實測測線產(chǎn)狀一致的虛擬測線獲取與之相交結(jié)構(gòu)面的傾向和傾角。為區(qū)分野外實測產(chǎn)狀,我們將從模型中獲取的產(chǎn)狀命名為“模型產(chǎn)狀”；第四,利用Kolmogorov-Smimov雙樣本檢驗法,測試不同網(wǎng)格大小下實測產(chǎn)狀與模型產(chǎn)狀的概率分布差異。 2.評價無網(wǎng)格化時的誤差量級。 (1)有必要測試無網(wǎng)格化的可行性。 (2)基于前述的實測產(chǎn)狀數(shù)據(jù)比較網(wǎng)格化與不網(wǎng)格化的誤差。利用糾偏結(jié)果構(gòu)建結(jié)構(gòu)面三維網(wǎng)絡模型,從模型中得到55個測量產(chǎn)狀數(shù)據(jù),用Kolmogorov-Smimov雙樣本檢驗法測試了原始產(chǎn)狀概率分布和模擬產(chǎn)狀概率分布之間的誤差。另一方面,利用結(jié)構(gòu)面隨機網(wǎng)絡模擬開展精度測試,此模擬與實測數(shù)據(jù)相比擁有更多測線產(chǎn)狀和樣本數(shù)的組合。第一,建立結(jié)構(gòu)面、露頭和測線模型,并且獲取與測線相交的結(jié)構(gòu)面產(chǎn)狀。為區(qū)分這些相交的產(chǎn)狀,巖體三維空間內(nèi)的產(chǎn)狀被稱為“原始產(chǎn)狀”。然后,利用Terzaghi方法,分別在網(wǎng)格化和非網(wǎng)格化的兩種情況下對獲取的產(chǎn)狀數(shù)據(jù)進行頻率糾偏。緊接著,用Kolmogorov-Smimov雙樣本檢驗法測試原始產(chǎn)狀和糾偏后產(chǎn)狀之間的概率分布差異。 (3)比較網(wǎng)格化與非網(wǎng)格化兩種情況下概率分布差異大小,如果非網(wǎng)格化差異較小,則討論非網(wǎng)格化代替網(wǎng)格化的可行性。 3.提出一種更更有效的糾偏方法。 (1)用積分方法推導產(chǎn)狀的概率密度函數(shù)(為數(shù)值解)。 (2)然后在此函數(shù)基礎上提出了包括2個假設和5個步驟的數(shù)值解法。 兩個假設是： (a)假設每一分組內(nèi)的產(chǎn)狀概率分布與直徑概率分布是相互獨立的； (b)假設在巖體三維空間中,每一分組內(nèi)的兩個產(chǎn)狀元素(傾向和傾角)概率分布是相互獨立的。同樣的假設也應適用于與測線或鉆孔相交的結(jié)構(gòu)面產(chǎn)狀。 五個步驟包括： (a)分組�？衫肈ips軟件實現(xiàn)。需注意的是每個分組都應各自進行分析和糾偏。 (b)檢驗傾向與傾角之間的獨立性。由前面假設可知傾向與傾角之間須保持獨立,因此有必要檢驗實測產(chǎn)狀的傾向與傾角是否滿足這個假設。獨立性測試方法有許多種,Pearson開方(x2)檢驗法就是其中之一。 (c)根據(jù)推導的數(shù)值解糾正傾向與傾角的概率分布。 (d)判斷糾偏后的產(chǎn)狀概率分布類型。 (e)計算修正后的產(chǎn)狀分布參數(shù)。此處參數(shù)選擇需先考慮概率分布類型,已經(jīng)由步驟4確定。例如,對于正態(tài)分布,參數(shù)為均值和標準差(或方差)；對于對數(shù)正態(tài)分布,參數(shù)為均值和對數(shù)標準差(或方差)；對于均勻分布,參數(shù)為下限和上限；對于指數(shù)分布,參數(shù)為均值。確定好參數(shù)形式后,可以利用Matlab或SPSS通過最小二乘法得到參數(shù)值。 對于步驟4,在一般的統(tǒng)計分析中,有兩種用于判斷概率分布類型的方式：從概率密度曲線形狀判斷或從累積分布曲線形狀判斷。為了在兩種方式之間選取較合適者,在4種產(chǎn)狀分布類型下比較兩種方式有效性。比較的程序如下： (a)不妨假定產(chǎn)狀和其他為建模所必需的參數(shù)(如大小、密度、張開度)。其中假設的產(chǎn)狀分布包括4種類型,分別為正態(tài)分布,對數(shù)正態(tài)分布,均勻分布和指數(shù)分布；為每種分布類型設定7種樣本數(shù),分別為50,100,150,200,300,500和1000。 (b)輸入這些參數(shù),采用隨機模擬方法建立結(jié)構(gòu)面的三維網(wǎng)絡模型。根據(jù)4種不同的概率分布,建立4個不同的結(jié)構(gòu)面網(wǎng)絡模型。 (c)獲取模型中與測線相交的結(jié)構(gòu)面的產(chǎn)狀數(shù)據(jù)。針對每種模型,采用7種不同的樣本數(shù)進行測量。因此,對于4中模型,共得到28個系列的產(chǎn)狀數(shù)據(jù)。 (d)由于提出的方法是基于實測傾向和傾角之間獨立性假設,因此,在糾偏前就得采用Pearson開方(x2)檢驗法測試此獨立性。 (e)為得到概率密度曲線,糾偏28個產(chǎn)狀系列；為得到累積分布曲線,也糾偏這些系列。然后對比兩者的有效性。 (3)利用前述實測產(chǎn)狀數(shù)據(jù)比較提出方法與Terzaghi方法的糾偏效果。 研究得到如下結(jié)論： 1.更詳細、合理地推導了Terzaghi的糾偏公式。推導過程中發(fā)現(xiàn),在盲區(qū)以外,Terzaghi方法由于公式中的近似替代而產(chǎn)生理論誤差。因此,為了提高糾偏效果,通過試驗和實例驗證給出了網(wǎng)格大小和樣本密度的建議值,即網(wǎng)格大小為2°×2°以及樣本密度為0.05°-2時誤差最小。 2.作為Terzaghi的方法一個內(nèi)部步驟,網(wǎng)格化投影圖往往會給糾偏結(jié)果引入一個相當大的誤差。試驗證明非網(wǎng)格化是可行的。最后,網(wǎng)格化與非網(wǎng)格化的糾偏結(jié)果準確性比較表明,糾偏結(jié)果在無網(wǎng)格化的情況下比在網(wǎng)格化時更精確。 3.在推導產(chǎn)狀在三維空間的概率分布函數(shù)的過程中,發(fā)現(xiàn)很難求取其解析解。所以推導出了數(shù)值近似解�；跀�(shù)值近似解,提出了包含兩個假設和五個步驟的產(chǎn)狀糾偏的數(shù)值解方法。 4.對于提出的方法,概率密度曲線和累積分布曲線的判斷分布類型效果對比顯示,根據(jù)概率密度曲線很難清楚地判斷產(chǎn)狀分布類型,相反地,可以很容易地從累積分布曲線中看出。這表明,在分布類型的判斷上,累積分布曲線比概率密度曲線更有效。所以相比于概率密度曲線和它的函數(shù)(概率密度函數(shù)),累積分布曲線和它的函數(shù)(累積分布函數(shù))是最佳分布形式判斷方式。 5.對于提出的方法,在各種樣本數(shù)下的糾偏效果對比試驗表明：(1)當傾向或傾角服從指數(shù)分布時,該方法是低效的。這說明該方法不適合指數(shù)分布的產(chǎn)狀。(2)當傾向或傾角服從均勻分布時該方法是相當有效的。且增加樣本數(shù)量幾乎不影響其效果。表明該方法適合均勻分布的產(chǎn)狀。(3)當產(chǎn)狀服從正態(tài)分布且樣本數(shù)量超過500,增加樣品數(shù)很難提高效果。所以應該限制樣本數(shù)量使其低于500。(4)當傾向或傾角服從對數(shù)正態(tài)分布且樣本數(shù)量超過150時,增加樣品數(shù)不能顯著提高效果。所以150為對數(shù)正態(tài)分布最佳的樣本數(shù)量。由于在測量和糾偏前未知分布類型,最佳樣本數(shù)量的判斷可能是上述四個情況之一。因此,結(jié)合上述四種結(jié)果后,為保證提出的方法高效性,最佳樣本數(shù)量應約為150。 6.與Terzaghi方法相比,提出的方法更有效。原因可能是Terzaghi方法是假設在每個計數(shù)圓里的所有結(jié)構(gòu)面是平行的。然而事實上,并不是所有的結(jié)構(gòu)面都是平行的。這種假設與事實的不符造成了Terzaghi方法低效。而提出的方法不基于這個假設,所以其糾偏效果會更高。
[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

【學位授予單位】：中國地質(zhì)大學
【學位級別】：博士
【學位授予年份】：2014
【分類號】：TU45

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