室内岩体结构面抗剪强度参数取值方法研究
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摘要
岩体由岩块和结构面组成,其中结构面的变形与强度性质往往对岩体的变形和稳定性起着决定性作用。结构面抗剪强度参数是岩体工程设计及计算的重要参数之一,但若要获得准确的结构面抗剪强度参数却异常困难,“参数给不准”已经成为岩石力学理论分析和数值模拟的瓶颈问题,因此研究岩体结构面抗剪强度参数优化选取方法具有重要的现实意义。
本文从结构面强度参数的不确定性出发,结合室内剪切试验,以Mohr-Coulomb强度准则为基础,通过试验数据处理方法、制样误差角效应及结构面抗剪强度修正、研制新型结构面直剪试验装置三个方面,提出优化选取结构面抗剪强度参数的方法和建议,达到了试验与数据处理方法相结合,从整个过程减小不确定性对试验结果影响的目的。
最小二乘法是室内结构面直剪试验数据处理常用方法,但其具有明显的理论缺陷,仅依靠该方法处理试验数据存在不足。受现场大型原位试验数据处理方法启发,将点群中心法、随机-模糊法、可靠度分析法引入室内结构面直剪试验数据处理方法中,以达到能根据试验数据情况、试验样本条件、工程参数要求等选择合适的方法进行求解的目的。
(1)最小二乘法的理论根源是平方和最小原理,该方法只考虑了试验样本的随机性,无法考虑参数的模糊性,受异常值的影响较大。但方法简单成熟,操作方便快捷,求解过程不受数据量限制,处理过程直观,无计算收敛问题。它适用于求解数据线性较好、异常点较少、试样数据较多的条件下使用,即便是其他分析方法失效时,仍可用其求解所得参数作为参考。
(2)点群中心法属于粗定结构面抗剪强度的方法,原理上与最小二乘法有类似之处,均可通过求解试验数据点到直线距离进行判断,但评价指标不一样。最显著的特征是操作简便,可手工绘制,处理过程最直观。但该方法理论立意不明确,对离散数据处理效果不理想,手工绘制结果因人而异。适用于数据线性较好,结构面抗剪强度的粗判；
(3)随机-模糊法从结构面本身性质出发,通过构建隶属度及隶属度函数,以“隶属度最大原则”为前提,通过迭代运算确定出抗剪强度参数的最佳估计。随机-模糊法较最小二乘法有较大的理论进步,其局限性在于隶属度函数的选择。此外,该方法还有求解相对繁琐、存在收敛问题等缺陷,适用于处理具有空间变异性或类属不确定性的变量。
(4)可靠度分析法考虑了结构面抗剪强度参数的概率分布特征,只需给定参数的保证率,就可以得到该保证率下抗剪强度参数的取值。但是,迭代过程中,赋初值对计算过程的收敛性及计算结果影响很大,迭代循环较复杂,此外还存在抗剪强度参数服从正态分布的假设。对于需指定参数保证率,粘聚力、内摩擦角参数统计大致服从正态分布规律,且相关性好、异常点(突出点)较少的情况较为适用,也可以用于处理试验数据较离散的情况。
此外,通过对四种试验数据处理方法定量计算对比分析发现：当试验数据线性较好时,4种试验数据处理方法都适用,最终结果相差不大,出于参数保守考虑,可以取较小值作为推荐参数；当数据量较大但较离散时,参数取值时不能使用点群中心法,而应采用其余3种方法进行求解,其中最小二乘法、随机-模糊法、可靠度分析法所得结果进行对比后,进行取值；当数据量较小且离散的情况时,点群中心法、最小二乘法处理结果不理想,而应主要参考随机-模糊法、可靠度分析法的结果。
结构面制样误差是本文另一讨论要点,主要从制样误差角对结构面抗剪强度影响分析、两种抗剪强度参数修正方法、数值模拟试验验证三个方面展开,所得结论如下：
(1)根据剪切方向及制样误差角的对应关系,确定出误差角控制因素倾角a、偏角β,推导得到“爬坡向”及“顺坡向”的正、剪应力修正公式。对比分析结构面制样误差角中倾角a、偏角β对结构面抗剪强度的影响程度,发现倾角a是控制结构面抗剪强度参数产生误差的关键性因素,而偏角β对其影响可忽略不计,进而得到简化后的正、剪应力修正公式。
(2)对常规试验条件下结构面制样误差角进行统计,发现结构面制样误差角服从正态分布特征,制样误差角α主要集中在0±5°的区间内。
(3)将正、剪应力修正公式代入Mohr-Coulomb公式,可分别得到“爬坡向”、“顺坡向”结构面抗剪强度修正公式,即利用统计得到的平均制样误差角直接对试验结果进行修正。这是结构面抗剪强度修正的另一种方法,该方法虽较第一种方法粗略,但不失为一种参数修正的简易方法。
(4)使用FLAC3D数值模拟软件,以无误差角条件为例,对结构面直剪试验进行数值模拟,验证了数值模拟方法的正确性及可行性。对偏角β=0。时,倾角分别为α=±1。α=±2°,α=±3°,α=±4°,α=±5°条件下,结构面直剪试验进行数值模拟对比发现：当荷载作用方向为“爬坡向”时,随着倾角α的增大,结构面的内摩擦角φ及粘聚力c都随之增大；当荷载作用方向为“顺坡向”时,随着倾角α的增大,结构面的内摩擦角φ及粘聚力c都随之减小。数值模拟结果与修正公式求解结果吻合的很好,验证了结构面制样误差效应及结构面抗剪强度修正公式的正确性。最后,以偏角β=5°,α=0。理想平直结构面为例,说明了误差角中倾角α是影响结构面抗剪强度的关键因素。
为解决传统便携式结构面试验仪的缺陷,研制出了新型便携式现场和室内两用岩体结构面直剪试验仪,提供了一种简洁、快速、方便、准确获得结构面强度参数的方法。试验装置主要有两部分组成：制样剪切盒及剪切装置。其中制样剪切盒,结构简单,操作方便,将结构面制样与剪切过程合二为一,使试验过程更为优化,保证了试验的准确性,消除了结构面制样误差角,最大程度的减小了人为因素对结构面的干扰。剪切装置的设计消除了传统结构面直剪仪会产生额外力偶、法向应力失真的问题。此外,本剪切装置还考虑了位移限制设计及复位装置,消除无效剪切位移对试验数据采集的影响。改进直剪试验CAT系统,实现正应力、剪应力、法向位移、剪切位移同步实时记录处理,集信号采集、信号处理、信号输出于一体。该装置仪器轻便,形状规则,拆装方便,便于携带,非常适合于在取样现场进行快速的结构面剪切试验。
最后,以陈家坝研究区结构面抗剪强度参数优化选取为例,提出优化求解结构面抗剪强度参数的一般步骤：正确、规范的结构面直剪试验→结构面抗剪强度参数的修正→多种方法试验数据处理对比分析后,确定结构面抗剪强度参数。并优化确定了该地区的结构面抗剪强度参数c、φ值。
Rock masses are composed of rock blocks and structural planes. The deformation and stability of rock mass is mainly controlled by structural plane's characters of deformation and strength. It is hard for us to get shear strength parameters of the structural planes exactly, which are important for rock mass designing and calculating. The inaccurate parameter is becoming the bottleneck problem of the theoretical analysis and numerical modeling for rock mess. Therefore, it is significant to research on determination methods of shear strength parameters of structural planes.
Considering the uncertainty of the structural planes'parameters and combined indoor shearing tests, we put forward methods and suggestions on optimizing the parameters from three ways, which are processing methods for test data, analyzing domino effect of sample preparation errors and correcting the structural planes'strength parameters, producing a new structural plane direct shear test apparatus. In this way, the influence to the test result may sharply be decreased from the whole process.
Least square method is commonly used for dealing with direct shear test data of the structural plane. When using least square method, some disadvantage appears due to the obvious theory limitations. Enlightened by situ-testing, point cluster center method, random-fuzziness method, reliability analysis method are used to manage the data in order to choose the right method due to the test data condition, test sample condition, engineering parameters requirements.
(1) Theoretical source of least square method is the theory of minimum squares which only consider the randomness of the test samples. It is suitable for solving the good linear, less abnormal points contained, large amount data. Even other method fails, it is still a available way for reference.
(2) Point cluster center method belongs to the methods of roughly determining the shear strength of structural plane which is similar to least square method. The parameters can be determined by solving the distance of the points to the line. The prominent feature of the method is easy operating, hand-painted, intuitive processing. It is suitable for solving good linear data and coarse determination of shear strength.
(3) The property of structure plane is the start point of random-fuzziness method. The best estimation is determined by iterative operation which chooses "Membership Maximum Principle" as the prerequisite. The comparison between random-fuzziness method and least square method shows the former is much more advanced, though it is limited by the difficulty of choosing the right membership function, complex calculation processes; convergence problems and so on. It is suitable to deal with the space variable quantity or generic uncertain quantity.
(4) Reliability analysis method takes the distribution characteristics of the shear strength parameters into account. The shear strength parameters can only be determined by given the assurance rate that we need. But it is difficult to set the initial value, because the result may changes with it. This method which must obey the normal distribution assumption also has the convergence problems and the complex calculation processes. It is suitable for dealing with the data which is given the assurance rate and contains less abnormal points, the parameters meeting normal distribution and good correlativity or the test data is discrete.
By quantitative calculation and comparison between the four methods, we can get the conclusions as follows:Firstly, when the test data is high linear, the calculated result by four methods is similar with each other; we can choose the smallest as the suggesting parameter for conservative consideration. And then, if the test data is enough but discrete, we should take the other three methods instead of to deal with the point cluster center method with the test data. The suggesting parameter is offered by comparing the different three results. Thirdly, if we meet with the test data which is not only scared but also discrete, the calculated results of least square method and point cluster center method are not satisfactory. We can mainly depend on the results calculated by random-fuzzy method and reliability analysis method.
Sample preparation errors is the second main point discussed in this paper which is introduced in three aspects, the great effects on shear strength caused by sample preparation errors, two methods for correcting parameters and the confirmation by numerical simulation test. Conclusions can be summarized as follows:
(1) The sample preparation errors are controlled by dip angleα, drift angleβwhich can be determined by shear direction and sample error angle. And the formula about correcting normal stress and shear stress is derived by that. The comparison about the influence on shear strength between dip angleα, drift angleβshows dip angle a plays much more important place than drift angleβdoes which can even be ignored. Then we can get the simplified formula about correcting normal stress and shear stress.
(2) We find dip angleαobeys normal distribution by statistic to the sample preparation errors under the normal test condition. The dip angleαis mainly near 0±5°.
(3) The structure plane's modifier formula of 'climbing direction' and 'downward direction' can be solved by putting the correcting normal stress and shear stress formula into Mohr-Coulomb formula. If given the mean angle of sample preparation errors, the result can be directly set right by this formula. Though this is a rough method, it gives easy way for making the parameter corrected.
(4) We simulate the direct shear test by FLAC3D numerical simulation software. It is certified correctly that the method used for simulating is absolutely right. Besides it is simulated under different conditions when drift angleβis 0°, dip angleαchanges fromα=±1°toα=±5°. The comparison shows the cohesion and friction angle of the joints increase or decrease with the dip angleα. The results calculated by numerical simulation and theory formula are extremely similar, which verifies the correctness of the theory formula. Finally, we choose the condition as en example when the drift angleβis 5°and the dip angleαis 0°.It shows the dip angle a is critical factor which controls the impress on the shear strength of the joints.
In this paper, we introduced a new apparatus for structure plane direct shear test which can be used indoor or outside. It offers easy, fast, convenience and veracious way for determining the parameters by using this apparatus. This apparatus can be divided into two parts:the box for making sample and shear testing, the shear equipment. The structure of the box is simple and easy for using. It can merge the process of making the sample and shearing in order to eliminate the influence caused by the sample preparation errors. It can extremely decrease impact to structure plane caused by the personal factor. The extra moment of couple and distortion of stress result from using the traditional apparatus. The invalid shear displacement is cleared up by limit displacement device and position restoration device. The improved direct shear system CAT can record the normal stress, the shear stress, the normal displacement and the shear displacement at the same time. It concentrates signal acquisition, signal processing and signal output. The apparatus is very suitable for fast outside direct shear test, because it is less heavy than traditional machines and it is easy for testing and taking with the regularly shape.
The general steps of optimal solution method are proposed by taking the joints shear strength determination in Chenjia dam as an example. Firstly, we should do the shear test in standard, correct way. Then the test data should be modified due to the structure plane's modifier formula. Ultimately, the parameter can be determined by comparing the results calculated by different methods.
本文从结构面强度参数的不确定性出发,结合室内剪切试验,以Mohr-Coulomb强度准则为基础,通过试验数据处理方法、制样误差角效应及结构面抗剪强度修正、研制新型结构面直剪试验装置三个方面,提出优化选取结构面抗剪强度参数的方法和建议,达到了试验与数据处理方法相结合,从整个过程减小不确定性对试验结果影响的目的。
最小二乘法是室内结构面直剪试验数据处理常用方法,但其具有明显的理论缺陷,仅依靠该方法处理试验数据存在不足。受现场大型原位试验数据处理方法启发,将点群中心法、随机-模糊法、可靠度分析法引入室内结构面直剪试验数据处理方法中,以达到能根据试验数据情况、试验样本条件、工程参数要求等选择合适的方法进行求解的目的。
(1)最小二乘法的理论根源是平方和最小原理,该方法只考虑了试验样本的随机性,无法考虑参数的模糊性,受异常值的影响较大。但方法简单成熟,操作方便快捷,求解过程不受数据量限制,处理过程直观,无计算收敛问题。它适用于求解数据线性较好、异常点较少、试样数据较多的条件下使用,即便是其他分析方法失效时,仍可用其求解所得参数作为参考。
(2)点群中心法属于粗定结构面抗剪强度的方法,原理上与最小二乘法有类似之处,均可通过求解试验数据点到直线距离进行判断,但评价指标不一样。最显著的特征是操作简便,可手工绘制,处理过程最直观。但该方法理论立意不明确,对离散数据处理效果不理想,手工绘制结果因人而异。适用于数据线性较好,结构面抗剪强度的粗判；
(3)随机-模糊法从结构面本身性质出发,通过构建隶属度及隶属度函数,以“隶属度最大原则”为前提,通过迭代运算确定出抗剪强度参数的最佳估计。随机-模糊法较最小二乘法有较大的理论进步,其局限性在于隶属度函数的选择。此外,该方法还有求解相对繁琐、存在收敛问题等缺陷,适用于处理具有空间变异性或类属不确定性的变量。
(4)可靠度分析法考虑了结构面抗剪强度参数的概率分布特征,只需给定参数的保证率,就可以得到该保证率下抗剪强度参数的取值。但是,迭代过程中,赋初值对计算过程的收敛性及计算结果影响很大,迭代循环较复杂,此外还存在抗剪强度参数服从正态分布的假设。对于需指定参数保证率,粘聚力、内摩擦角参数统计大致服从正态分布规律,且相关性好、异常点(突出点)较少的情况较为适用,也可以用于处理试验数据较离散的情况。
此外,通过对四种试验数据处理方法定量计算对比分析发现：当试验数据线性较好时,4种试验数据处理方法都适用,最终结果相差不大,出于参数保守考虑,可以取较小值作为推荐参数；当数据量较大但较离散时,参数取值时不能使用点群中心法,而应采用其余3种方法进行求解,其中最小二乘法、随机-模糊法、可靠度分析法所得结果进行对比后,进行取值；当数据量较小且离散的情况时,点群中心法、最小二乘法处理结果不理想,而应主要参考随机-模糊法、可靠度分析法的结果。
结构面制样误差是本文另一讨论要点,主要从制样误差角对结构面抗剪强度影响分析、两种抗剪强度参数修正方法、数值模拟试验验证三个方面展开,所得结论如下：
(1)根据剪切方向及制样误差角的对应关系,确定出误差角控制因素倾角a、偏角β,推导得到“爬坡向”及“顺坡向”的正、剪应力修正公式。对比分析结构面制样误差角中倾角a、偏角β对结构面抗剪强度的影响程度,发现倾角a是控制结构面抗剪强度参数产生误差的关键性因素,而偏角β对其影响可忽略不计,进而得到简化后的正、剪应力修正公式。
(2)对常规试验条件下结构面制样误差角进行统计,发现结构面制样误差角服从正态分布特征,制样误差角α主要集中在0±5°的区间内。
(3)将正、剪应力修正公式代入Mohr-Coulomb公式,可分别得到“爬坡向”、“顺坡向”结构面抗剪强度修正公式,即利用统计得到的平均制样误差角直接对试验结果进行修正。这是结构面抗剪强度修正的另一种方法,该方法虽较第一种方法粗略,但不失为一种参数修正的简易方法。
(4)使用FLAC3D数值模拟软件,以无误差角条件为例,对结构面直剪试验进行数值模拟,验证了数值模拟方法的正确性及可行性。对偏角β=0。时,倾角分别为α=±1。α=±2°,α=±3°,α=±4°,α=±5°条件下,结构面直剪试验进行数值模拟对比发现：当荷载作用方向为“爬坡向”时,随着倾角α的增大,结构面的内摩擦角φ及粘聚力c都随之增大；当荷载作用方向为“顺坡向”时,随着倾角α的增大,结构面的内摩擦角φ及粘聚力c都随之减小。数值模拟结果与修正公式求解结果吻合的很好,验证了结构面制样误差效应及结构面抗剪强度修正公式的正确性。最后,以偏角β=5°,α=0。理想平直结构面为例,说明了误差角中倾角α是影响结构面抗剪强度的关键因素。
为解决传统便携式结构面试验仪的缺陷,研制出了新型便携式现场和室内两用岩体结构面直剪试验仪,提供了一种简洁、快速、方便、准确获得结构面强度参数的方法。试验装置主要有两部分组成：制样剪切盒及剪切装置。其中制样剪切盒,结构简单,操作方便,将结构面制样与剪切过程合二为一,使试验过程更为优化,保证了试验的准确性,消除了结构面制样误差角,最大程度的减小了人为因素对结构面的干扰。剪切装置的设计消除了传统结构面直剪仪会产生额外力偶、法向应力失真的问题。此外,本剪切装置还考虑了位移限制设计及复位装置,消除无效剪切位移对试验数据采集的影响。改进直剪试验CAT系统,实现正应力、剪应力、法向位移、剪切位移同步实时记录处理,集信号采集、信号处理、信号输出于一体。该装置仪器轻便,形状规则,拆装方便,便于携带,非常适合于在取样现场进行快速的结构面剪切试验。
最后,以陈家坝研究区结构面抗剪强度参数优化选取为例,提出优化求解结构面抗剪强度参数的一般步骤：正确、规范的结构面直剪试验→结构面抗剪强度参数的修正→多种方法试验数据处理对比分析后,确定结构面抗剪强度参数。并优化确定了该地区的结构面抗剪强度参数c、φ值。
Rock masses are composed of rock blocks and structural planes. The deformation and stability of rock mass is mainly controlled by structural plane's characters of deformation and strength. It is hard for us to get shear strength parameters of the structural planes exactly, which are important for rock mass designing and calculating. The inaccurate parameter is becoming the bottleneck problem of the theoretical analysis and numerical modeling for rock mess. Therefore, it is significant to research on determination methods of shear strength parameters of structural planes.
Considering the uncertainty of the structural planes'parameters and combined indoor shearing tests, we put forward methods and suggestions on optimizing the parameters from three ways, which are processing methods for test data, analyzing domino effect of sample preparation errors and correcting the structural planes'strength parameters, producing a new structural plane direct shear test apparatus. In this way, the influence to the test result may sharply be decreased from the whole process.
Least square method is commonly used for dealing with direct shear test data of the structural plane. When using least square method, some disadvantage appears due to the obvious theory limitations. Enlightened by situ-testing, point cluster center method, random-fuzziness method, reliability analysis method are used to manage the data in order to choose the right method due to the test data condition, test sample condition, engineering parameters requirements.
(1) Theoretical source of least square method is the theory of minimum squares which only consider the randomness of the test samples. It is suitable for solving the good linear, less abnormal points contained, large amount data. Even other method fails, it is still a available way for reference.
(2) Point cluster center method belongs to the methods of roughly determining the shear strength of structural plane which is similar to least square method. The parameters can be determined by solving the distance of the points to the line. The prominent feature of the method is easy operating, hand-painted, intuitive processing. It is suitable for solving good linear data and coarse determination of shear strength.
(3) The property of structure plane is the start point of random-fuzziness method. The best estimation is determined by iterative operation which chooses "Membership Maximum Principle" as the prerequisite. The comparison between random-fuzziness method and least square method shows the former is much more advanced, though it is limited by the difficulty of choosing the right membership function, complex calculation processes; convergence problems and so on. It is suitable to deal with the space variable quantity or generic uncertain quantity.
(4) Reliability analysis method takes the distribution characteristics of the shear strength parameters into account. The shear strength parameters can only be determined by given the assurance rate that we need. But it is difficult to set the initial value, because the result may changes with it. This method which must obey the normal distribution assumption also has the convergence problems and the complex calculation processes. It is suitable for dealing with the data which is given the assurance rate and contains less abnormal points, the parameters meeting normal distribution and good correlativity or the test data is discrete.
By quantitative calculation and comparison between the four methods, we can get the conclusions as follows:Firstly, when the test data is high linear, the calculated result by four methods is similar with each other; we can choose the smallest as the suggesting parameter for conservative consideration. And then, if the test data is enough but discrete, we should take the other three methods instead of to deal with the point cluster center method with the test data. The suggesting parameter is offered by comparing the different three results. Thirdly, if we meet with the test data which is not only scared but also discrete, the calculated results of least square method and point cluster center method are not satisfactory. We can mainly depend on the results calculated by random-fuzzy method and reliability analysis method.
Sample preparation errors is the second main point discussed in this paper which is introduced in three aspects, the great effects on shear strength caused by sample preparation errors, two methods for correcting parameters and the confirmation by numerical simulation test. Conclusions can be summarized as follows:
(1) The sample preparation errors are controlled by dip angleα, drift angleβwhich can be determined by shear direction and sample error angle. And the formula about correcting normal stress and shear stress is derived by that. The comparison about the influence on shear strength between dip angleα, drift angleβshows dip angle a plays much more important place than drift angleβdoes which can even be ignored. Then we can get the simplified formula about correcting normal stress and shear stress.
(2) We find dip angleαobeys normal distribution by statistic to the sample preparation errors under the normal test condition. The dip angleαis mainly near 0±5°.
(3) The structure plane's modifier formula of 'climbing direction' and 'downward direction' can be solved by putting the correcting normal stress and shear stress formula into Mohr-Coulomb formula. If given the mean angle of sample preparation errors, the result can be directly set right by this formula. Though this is a rough method, it gives easy way for making the parameter corrected.
(4) We simulate the direct shear test by FLAC3D numerical simulation software. It is certified correctly that the method used for simulating is absolutely right. Besides it is simulated under different conditions when drift angleβis 0°, dip angleαchanges fromα=±1°toα=±5°. The comparison shows the cohesion and friction angle of the joints increase or decrease with the dip angleα. The results calculated by numerical simulation and theory formula are extremely similar, which verifies the correctness of the theory formula. Finally, we choose the condition as en example when the drift angleβis 5°and the dip angleαis 0°.It shows the dip angle a is critical factor which controls the impress on the shear strength of the joints.
In this paper, we introduced a new apparatus for structure plane direct shear test which can be used indoor or outside. It offers easy, fast, convenience and veracious way for determining the parameters by using this apparatus. This apparatus can be divided into two parts:the box for making sample and shear testing, the shear equipment. The structure of the box is simple and easy for using. It can merge the process of making the sample and shearing in order to eliminate the influence caused by the sample preparation errors. It can extremely decrease impact to structure plane caused by the personal factor. The extra moment of couple and distortion of stress result from using the traditional apparatus. The invalid shear displacement is cleared up by limit displacement device and position restoration device. The improved direct shear system CAT can record the normal stress, the shear stress, the normal displacement and the shear displacement at the same time. It concentrates signal acquisition, signal processing and signal output. The apparatus is very suitable for fast outside direct shear test, because it is less heavy than traditional machines and it is easy for testing and taking with the regularly shape.
The general steps of optimal solution method are proposed by taking the joints shear strength determination in Chenjia dam as an example. Firstly, we should do the shear test in standard, correct way. Then the test data should be modified due to the structure plane's modifier formula. Ultimately, the parameter can be determined by comparing the results calculated by different methods.
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