Prediction and density calculation of complex structural plane features of fractured rock mass
MA Jun1，2，TAN Chun1，2，MA Zhifa1，2，WANG Changyi1，2，ZHANG Wen3
(1. China Water Northeastern Investigation，Design and Research Co.，Ltd.，Changchun，Jilin 130000，China；2. Engineering Technology Research Center of Ministry of Water Resource in the Cold Region，Changchun，Jilin 130000，China；3. College of Construction Engineering，Jilin University，Changchun，Jilin 130000，China)
Abstract：Fracture systems are always covered by accumulations，resulting in blank information on rock mass structures. Thus，the accuracy of rock mass structure analysis is tremendously decreased. This paper aims to establish a regular and complete fracture information region as well as a simple calculation method for three-dimensional(3D) fracture density，which benefit fine descriptions of rock mass structures. Specifically，this paper introduced geostatistical method to predict fractures in blank areas based on spatial geometric parameter correlations of collected fractures. Consequently，the global distribution characteristics of two-dimensional(2D) fractures in a regular region were determined. Based on the aforementioned results，3D fracture network models were established. Subsequently，conception of 3D statistical fracture density was proposed based on probability thoughts；then，density was determined based on spatial intersection trial method. Through comparison between in-situ and modeled half-trace probability density curves，rationality of fracture prediction in blank areas and 3D fracture density calculation were verified. In sum，these methods are able to obtain complete 2D fracture characteristics and significantly simplify 3D fracture network modeling procedures. Consequently，accuracy and efficiency of rock mass structure analysis can be improved.
马 军1，2，谭 春1，2，马智法1，2，王常义1，2，张 文3. 裂隙岩体复杂结构面特征预测与密度计算[J]. 岩石力学与工程学报, 2021, 40(S2): 3127-3136.
MA Jun1，2，TAN Chun1，2，MA Zhifa1，2，WANG Changyi1，2，ZHANG Wen3. Prediction and density calculation of complex structural plane features of fractured rock mass. , 2021, 40(S2): 3127-3136.
[1] DERSHOWITZ W S，EINSTEIN H H. Characterizing rock joint geometry with joint system models[J]. Rock Mechanics and Rock Engineering，1988，21：21–51.
[2] 孙洪泉. 地质统计学及其应用[M]. 徐州：中国矿业大学出版社，1990：1–6.(SUN Hongquan. Geostatistics and its applications[M]. Xuzhou：China University of Mining and Technology Press，1990：1–6.(in Chinese))
[3] MATHERON G. The theory of regionalized variables and its applications[M]. Paris：Ecole Nationale Supérieure des Mines，1971：1–6.
[4] ESFAHANI N M，ASGHARI O. Fault detection in 3D by sequential gaussian simulation of rock quality designation(RQD)[J]. Arabian Journal of Geosciences，2013，12(10)：3 737–3 747.
[5] OZTURK CA，NASUF E. Geostatistical assessment of rock zones for tunneling[J]. Tunnelling and Underground Space Technology，2002，17：275–285.
[6] FERRARI F，APUANI T，GIANI G P. Rock mass rating spatial estimation by geostatistical analysis[J]. International Journal of Rock Mechanics and Mining Sciences，2014，70：162–176.
[7] EXADAKTYLOS G，STAVROPOULOU M. A specific upscaling theory of rock mass parameters exhibiting spatial variability：analytical relations and computational scheme[J]. International Journal of Rock Mechanics and Mining Sciences，2008，45(7)：1 102–1 125.
[8] MARISA P，JAVIER V. Geostatistical simulation to map the spatial heterogeneity of geomechanical parameters：a case study with rock mass rating[J]. Environmental Geology，2016，205：93–103.
[9] ELLEFMO S L，EIDSVIK J. Local and spatial joint frequency uncertainty and its application to rock mass characterisation[J]. Rock Mechanics and Rock Engineering，2009，42(4)：667–668.
[10] DEISMAN N，KHAJEH M，CHALATURNYK R J. Using geological strength index(GSI) to model uncertainty in rock mass properties of coal for CBM/ECBM reservoir geomechanics[J]. International Journal of Coal Geology，2013，112：76–86.
[11] OZTURK C A，SIMDI E. Geostatistical investigation of geotechnical and constructional properties in kadikoy-kartal subway[J]. Tunnelling and Underground Space Technology，2014，4：35–45.
[12] YOUNG D S. Indicator Kriging for unit vectors：rock joint orientations[J]. Mathematical Geology，1987，19：481–501.
[13] KOSASIH W，RASOULI V. Geostatistical analysis of surface morphology and its relationship with hydro-mechanical properties of natural fractures[J]. Petroleum and Mineral Resources，2012，81：209–219.
[14] BLESSENT D. Stochastic fracture rock facies for groundwater flow modeling[J]. Dyna，2013，182：88–94.
[15] KOIKE K，KUBO T. 3D geostatistical modeling of fracture system in a granitic massif to characterize hydraulic properties and fracture distribution[J]. Tectonophysics，2015，660：1–16.
[16] LEI Q H，LATHAM J，TSANG C，XIANG JS，LANG P. A new approach to upscaling fracture network models while preserving geostatistical and geomechanical characterisitcs[J]. Journal of Geophysical Research：Solid Earth，2015，120(2)：4 784–4 807.
[17] 刘春学，倪春中，燕永锋，等. 利用地质统计学方法模拟岩石裂隙网络的三维空间分布——以云南个旧高松矿田为例[J]. 地球学报，2013，34(3)：347–353.(LIU Chunxue，NI Chunzhong，YAN Yongfeng，et al. Three-dimensional simulation of rock fractures by geostatistical method：a case study of Gaosong field in Yunnan Province[J]. Acta Geoscientica Sinica，2013，34(3)：347–353.(in Chinese))
[18] 王 鹏，李晓昭，章杨松，等. 基于GIS的甘肃北山花岗岩裂隙密度地质统计分析[J]. 工程地质学报，2013，21(1)：115–122.(WANG Peng，LI Xiaozhao，ZHANG Yangsong，et al. GIS based geostatistical analysis of fracture density of rock in Beishan area Gansu Province[J]. Journal of Engineering Geology，2013，21(1)：115–122.(in Chinese))
[19] SKEMPTON A W，SCHUSTER R L，PETLEY D J. Joints and fissures in the London clay at wraysburg and edgware[J]. Geotechnique，1969，19：205–217.
[20] ROGERS S，ELMO D，WEBB G，CATALAN A. Volumetric fracture intensity measurement for improved rock mass characterisation and fragmentation assessment in block caving operations[J]. Rock Mechanics and Rock Engineering，2015，48：633–649.
[21] LAVOINE E，DAVY P，DARCEL C，et al. On the density variability of Poissonian discrete fracture networks，with application to power-law fracture size distributions[J]. Advances in Geosciences，2019，49：77–83.
[22] KULATILAKE P H S W. WATHUGALA D N，STEPHANSSON O. Joint network modeling with a validation exercise in stripa mine Sweden[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1993，30(5)：503–526.
[23] 王 辉，钱海涛. 节理化岩体结构面分布密度的确定方法及其应用[J]. 地球与环境，2005，33(增1)：124–129.(WANG Hui，QIAN Haitao. The technique and application of assessing the distributing density of structures in rock mass[J]. Earth and Environment，2005，33(Supp.1)：124–129.(in Chinese))
[24] 周福军，陈剑平，徐黎明. 基于岩体不连续面三维分形维岩体质量评价研究[J]. 岩土力学，2012，33(8)：2 315–2 322.(ZHOU Fujun，CHEN Jianping，XU Liming. Study of rock masses quality evaluation based on 3D fractal dimension of rock discontinuity distribution[J]. Rock and Soil Mechanics，2012，33(8)：2 315–2 322.(in Chinese))
[25] SHANLEY R J，MAHTAB M A. Delineation and analysis of clusters in orientation data[J]. Mathematical Geo1ogy，1976，8(3)：9–23.
[26] HUDSON J A，PRIEST S D. Discontinuity frequency in rock mass[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1983，20(2)：75–89.
[27] KULATILAKE P H S W，WU T H. Estimation of mean trace length of discontinuities[J]. Rock Mechanics and Rock Engineering，1984，17(4)：215–32.
[28] TERZAGHI R D. Sources of error in joint surveys[J]. Geotechnique，1965，15(3)：287–304.
[29] 陈剑平，肖树芳，王 清. 随机不连续面三维网络计算机模拟原理[M]. 长春：东北师范大学出版社，1995：234–266.(CHEN Jianping，XIAO Shufang，WANG Qing. Modeling principle for stochastic three-dimensional discontinuity network[M]. Changchun：Northeast Normal University Press，1995：234–266.(in Chinese))
2021, Vol. 40 
