工程地质学报  2018, Vol. 26 Issue (5): 1336-1341   (#KB#)    
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  • 收稿日期:2018-06-14
  • 接受日期:2018-07-19
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    张国彪
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    陶悦

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    张国彪, 包含, 兰恒星, 等. 2018. 结构面粗糙度系数与采样精度的关系研究[J]. 工程地质学报, 26(5): 1336-1341. doi: 10.13544/j.cnki.jeg.2018248.
    ZHANG Guobiao, BAO Han, LAN Hengxing, et al. 2018. Research on the relationship between joint roughness coefficient and sampling precision of structural plane[J]. Journal of Engineering Geology, 26(5): 1336-1341. doi: 10.13544/j.cnki.jeg.2018248.

    结构面粗糙度系数与采样精度的关系研究
    张国彪, 包含, 兰恒星, 晏长根, 陶悦    
    ① 长安大学公路学院 西安 710064;
    ② 长安大学地测学院 西安 710054
    摘要:结构面粗糙度系数(JRC)的获取过程中存在采样精度问题,为了获取合理的JRC值,本文开展了JRC剖面线采样点精度研究。选取3种岩石,每种取10个具有一定粗糙程度的结构面为研究对象,运用三维激光扫描技术获取结构面几何形貌特征并进行数字化处理。在此基础上,提取结构面选定剖面线的起伏信息,利用分形理论计算不同采样点间隔条件下剖面线的JRC值,分析JRC取值中存在的采样点间隔效应,并研究其影响因素。结果发现:JRC值受剖面线采样点间隔影响,当采样点间隔小于临界间隔值时,JRC值基本保持不变;当间隔大于临界间隔值时JRC值出现波动。采样点临界间隔值与结构面粗糙程度相关,与JRC值呈负指数函数关系,并且其关系受岩石类型影响,岩石颗粒越小两者拟合度越高。综合3种岩石得到JRC值与采样点临界间隔值关系服从y=1.8314e-0.067x的函数分布,可以此为依据进行采样点临界间隔定量取值,来消除间隔效应对JRC值的影响。该项研究成果可为结构面粗糙信息采集提供科学的方法,通过选取合理的采样点数量,保证结构面信息采集工作效率和JRC值计算精度。
    关键词结构面粗糙度系数    三维激光扫描    采样点间隔    负指数关系    
    RESEARCH ON THE RELATIONSHIP BETWEEN JOINT ROUGHNESS COEFFICIENT AND SAMPLING PRECISION OF STRUCTURAL PLANE
    ZHANG Guobiao, BAO Han, LAN Hengxing, YAN Changgen, TAO Yue    
    ① School of Highway, Chang'an University, Xi'an 710064;
    ② School of Geological Engineering and Geometrics, Chang'an University, Xi'an 710054
    Abstract: The roughness of rock structure plane affects its shear strength. The joint roughness coefficient(JRC)has been widely used as a roughness parameter. However, there are sampling precision problems existing in the acquisition of JRC values. In order to obtain reasonable JRC values, this paper conducts a study on the precision of JRC profile sampling. 10 structure planes of sandstone, diorite and granite with a size of 10 cm ·10 cm are selected as study objects, respectively. A hand-held 3D laser scanner is used to scan the structure plane surface to obtain its geometric features. Digital processing is carried out with the help of 3D morphological image post-processing software. On the basis of this, fractal theory is selected to calculate JRC values under different sampling point spacing conditions. Then sampling point interval effects on JRC value is analyzed and its influencing factors are studied. Results show that:JRC values are affected mainly by the sample point interval on profile line. However, when the sampling interval is less than a certain critical value, the JRC basically remains unchanged. The critical interval of sampling point is related to the roughness of structural plane and has a negative exponential relation with the JRC values. In addition, the negative exponential relation is influenced by rock type. The smaller the rock particles are, the better the imitative effect is. When the three types of rock are considered comprehensively, a negative exponential function y=1.8314e-0.067x is obtained between the critical interval of sampling point and JRC value. So, to remove the interval effects on the JRC evaluation, the critical interval of sampling points can be quantified according to the function. This study can provide a scientific method for the collection of roughness information of structural plane. And the precision and efficiency of structural plane information collection can be ensured by selecting a reasonable number of sampling points.
    Key words: Joint roughness coefficient    3D laser scanning    Sampling interval    Negative exponential    

    0 引言

    在地质历史发展过程中,岩体在多因素作用下产生不同粗糙程度的结构面,而结构面的粗糙性直接影响了结构面的各向异性力学行为(Yang et al., 2001; 郭松峰等,2016尹晓萌等,2017)。深入开展结构面粗糙性的量化研究工作对解析岩体力学特性具有重要的意义(夏才初等,2002Andrade et al., 2008江洎洧等,2012)。结构面粗糙度系数(JRC)作为描述结构面粗糙程度的参数被广为应用。常规获取JRC的方法一般通过轮廓仪描绘结构面起伏状态并与Barton 10条标准JRC剖面线进行对比得出(Barton,1973Barton et al., 1977),但是这种方法受人为因素干扰较大,取值精确度不足。分形理论的引入为结构面形态精确描述提供了依据(Mandelbrot, 1977, 1983, Mandelbrot et al., 1984),可通过分形维数D计算获得较为准确的JRC值(谢和平等,1994谢和平, 1995, 1996)。随着三维激光扫描仪器的发展,利用三维激光扫描技术获得精确的结构面形貌特征图像已变得切实可行(Gordon et al., 2001Lemmens,2011)。基于扫描图像分析处理,结合分形理论,取得数据进行JRC值的计算,使得取值精度进一步提高。

    JRC值的获取方法一直在进步但仍有许多问题。计算某一区域的JRC值时需要获得相关的剖面线进行取点计算,但是剖面线上采样点间隔取值时由于没有统一的标准,使得结果代表性和精确性不足。近年来众多学者针对这一问题进行了研究。夏才初(1996)提出采样点间隔效应的概念,并探究了坡度均方根和高度均方根等形态参数随着间隔的变化,指出形态参数随着取样间隔的增大呈现出减小的趋势。Li et al. (2015)在研究岩石断裂面分形维数与粗糙度系数JRC的关系时,同样选取不同间隔剖面线进行了研究,印证了间隔效应的存在。基于此,Kulatilake et al. (1997)运用线性缩放的方法,提出尺寸范围这一新概念,Jang et al. (2014)进行了实际验证。Lee et al.(1990)以2mm、4mm、6mm、8mm、10 mm 5个采样间隔来分别计算分形维数D,发现不同间隔下获得的D值具有差异性,且分形维数D与不连续结构面粗糙度系数呈正相关。Bae et al. (2011)在采样间隔依次为1 mm、2 mm、4 mm、8 mm、16 mm、32 mm、64 mm时,获得分形维数D值,并与JRC值建立联系,发现不同间隔下JRC值不同。以上研究证实采样点间隔影响JRC的取值,但是受迫于采集技术的限制,无法进行结构面三维形貌的获取使得结果精确性不足。

    近年来,三维激光扫描成为了结构面高精度测量的首选方法。何秉顺等(2007)对自动化和半自动化两种三维激光扫描方法进行了研究,分析了两者的原理以及适用范围。葛云峰等(2015)运用三维激光扫描技术获取结构面几何信息,发现结构面粗糙程度与剪切过程中产生的热量成正比,并在此基础上提出了以能量为依据的结构面粗糙程度评价方法。唐志成等(2015)利用岩石三维表面形貌仪对节理面扫描,运用节理形貌描述方法得出节理粗糙度值与采样间隔呈负相关关系。宋磊博等(2017)运用三维白面扫描系统对3种不同粗糙程度的岩石测量,得到0.1 mm、0.2 mm……1.5 mm 15种采样间隔的点云数据。在此基础上,研究了常用的2D、3D形态表示参数在不同间距下的变化情况,发现参数随着间距增大而减小,并与采样间隔存在二次多项式的拟合关系。

    上述研究虽然获得了一些关于JRC采样点取值间隔效应的规律,但这些研究无法给定可以获得稳定JRC值的采样点间隔,且对于采样点间隔效应的影响因素没有进行具体的分析。为了定量的描述采样点间隔效应,获取更为精确的能描述结构面形貌特征的JRC值,本文运用高精度三维激光扫描仪进行结构面形貌特征扫描,在扫描的基础上对结构面信息进行数字化处理。借助相关软件提取结构面形态特征数据,并使用以分形理论为基础的JRC值计算公式取得可靠的JRC值,以此为基础对剖面线上采样点间隔进行研究。另外,分析相关的影响因素来获得反映结构面特征的JRC值,为研究岩体结构面力学性能提供可靠的参数。

    1 材料与方法
    1.1 结构面采集与形貌获取

    为了研究不同岩性、不同结构面粗糙程度下的JRC取值间隔效应,本次选用闪长岩、砂岩以及花岗岩3种岩石,各类型岩石选取10个具有一定粗糙区分度(表面起伏高度为0~6 mm),并且尺寸范围满足10 cm×10 cm的剪切结构面作为研究对象。显微镜观察发现选取的结构面矿物晶体表面擦痕较多且具有明显的方向性,可准确判断结构面受剪方向。以剪切方向(图 1红色箭头)为依据,确定起伏方向,从而保证剖面线选取的一致性。利用手持式三维激光扫描仪(Handyscan 3D,精度0.01 mm)获取各结构面形貌特征,选定区域并提取区域形貌信息作为结构面粗糙程度分析的基础(图 2)。

    图 1 结构面镜面擦痕 Fig. 1 Mirror scratches on structural plane

    图 2 结构面扫描及研究区选定 Fig. 2 Structural plane scanning and study area selecting

    1.2 结构面数字化与JRC计算原理

    运用Geomagic Studio对所扫描的结构面进行处理,获得结构面样本的形貌信息。以结构面剪切方向为依据确定剖面线延伸方向,并选定起始点截取10 cm长剖面线。提取剖面线数字化信息,获得剖面线上各点的坐标值。

    考虑到结构面起伏的非几何特性,适合运用分形理论来进行JRC值的计算。借助分形维数D以及D-JRC (谢和平等,1994)建立的函数关系求得结构面粗糙性系数JRC

    分形维数:

    $ D = \frac{{\lg 4}}{{\lg \left\{ {2\left[ {1 + \cos \;{\rm{arc}}\;\tan \left({2h/L} \right)} \right]} \right\}}} $ (1)

    结构面粗糙度系数:

    $ JRC = 85.2671{\left({D - 1} \right)^{0.5679}} $ (2)

    式(1)中,h为结构面平均起伏差;L为平均基线长度。

    2 JRC取值采样点间隔效应

    在所选取的3种岩石中,以闪长岩为例,在10个闪长岩结构面上选取具有一定区分度的10条剖面线并进行1~10编号。在此基础上运用Geomagic studio依次对选出的10条剖面进行采样点间隔划定,采样点间隔值依次选取0.1 mm、0.2 mm、……1.9 mm、2 mm(图 3)。根据不同采样点间隔下获得的点坐标,运用式(1)、式(2)得到对应点间隔下10条剖面线的JRC值。获得的相关数据如表 1所示。

    图 3 剖面线选定及剖面线上间隔点布置 Fig. 3 Selection of profile lines and interval points on profile lines distribution

    表 1 不同采样点间隔下10条剖面线JRC Table 1 JRC values of 10 profile lines under different sampling point interval

    通过数据可以发现,不同采样点间隔对应的JRC值呈现出非稳定性。为方便观察每条剖面线JRC值的变化情况作图 4

    图 4 不同采样点间隔下JRC值变化 Fig. 4 The change of JRC values under different sampling point interval

    图 4中可以看出,采样点间隔由小到大依次变化时,10条剖面线对应的JRC值先表现出一定的稳定性,随着点间隔继续增大到某一值(三角号标注)时JRC值表现出较大的波动性,证实了采样点间隔效应的存在。定义这一值为采样点临界间隔值。针对这一发现,对花岗岩和砂岩进行相同的研究,发现同样具有临界间隔值。依据3种岩石下每条选定的剖面线采样点临界间隔值与剖面线JRC值作图 5

    图 5 不同岩石采样点临界间隔值与JRC值函数关系 Fig. 5 The function relations between critical interval of sampling point and JRC values under different kinds of rock a.花岗岩;b.闪长岩;c.砂岩

    通过图 5可以发现采样点临界间隔值与其对应JRC值呈负指数函数关系。考虑到负指数函数的特征,可以认为,伴随着结构面粗糙程度的降低,采样点临界间隔值呈增大的趋势。

    3 采样点间隔效应影响因素分析

    以岩性和结构面粗糙程度两个方面来分析采样点间隔效应影响因素。

    考虑岩性的影响,以3种岩石情况下以JRC值为横坐标采样点临界间隔值为纵坐标作图 6,由图可以看出获得的函数均服从负指数函数分布但其拟合度具有一定的差别。针对这一现象,运用扫描电镜对选用的3种岩石进行了扫描,得到3种岩石的颗粒大小,花岗岩>闪长岩>砂岩。由图 6可知R砂岩2R闪长岩2R花岗岩2,可以认为岩体颗粒与拟合函数有关,颗粒越小函数拟合度越高。但是每种岩石差别不大,拟合度都在90%以上。

    图 6 岩石类型对采样点临界间隔值的影响 Fig. 6 Effects on the critical interval value of the sampling point under different kinds of rock

    综合3种岩石所得JRC值与采样点临界间隔之间关系,可得图 7。由图可知,在忽略岩石种类情况下,JRC值与采样点临界间隔值之间的负指数函数关系仍然具有90%以上的拟合度。可以认为粗糙程度与采样点临界间隔存在负指数函数关系,其对应的公式为y=1.8314e-0.067x,其中,y为点间隔,x为对应的JRC值,由于这一关系综合考虑了3种岩石的影响,因此具有较强的普适性。由此,可以依据此关系式,估算不同粗糙程度岩石的采样点临界间隔值,从而科学地消除采样点间隔效应。从函数关系来看,随着结构面粗糙程度变大,其对应的剖面线采样点临界间隔值减小,为精确获取结构面粗糙特征所需的采样点越多;反之,结构面粗糙程度越少,则所需的采样点数量越小。该关系式可为结构面粗糙信息采集提供科学方法,从而保证JRC取值精度和工作效率。

    图 7 JRC值对采样点临界间隔值的影响 Fig. 7 Effects of JRC value on the evaluation of critical interval of the sampling point

    4 结论

    (1) 结构面粗糙度系数JRC的取值受剖面线采样点间隔影响。采样点临界间隔值与其对应JRC值服从负指数函数关系。

    (2) 岩性对JRC值与采样点临界间隔的负指数函数关系有一定影响,岩石颗粒越小两者负指数函数关系越明显。

    (3) 通过对不同粗糙程度的岩体结构面分析,获得JRC值与其采样点临界间隔值的通用函数关系y=1.8314e-0.067x,在此基础上,可以进行采样点临界间隔量化取值,以便消除JRC值间隔效应的影响,并保证结构面信息采集工作效率和JRC值计算精度。

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