Article(id=1311999380052336675, tenantId=1146029695717560320, journalId=1311385891987619962, issueId=1311998530802250506, articleNumber=null, orderNo=null, doi=10.12090/j.issn.1006-6616.2025039, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1744128000000, receivedDateStr=2025-04-09, revisedDate=1761494400000, revisedDateStr=2025-10-27, acceptedDate=1763913600000, acceptedDateStr=2025-11-24, onlineDate=1790734627974, onlineDateStr=2026-09-30, pubDate=1787846400000, pubDateStr=2026-08-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1790734627974, onlineIssueDateStr=2026-09-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1790734627974, creator=13701087609, updateTime=1790734627974, updator=13701087609, issue=Issue{id=1311998530802250506, tenantId=1146029695717560320, journalId=1311385891987619962, year='2026', volume='32', issue='4', pageStart='771', pageEnd='998', issueExtLink='null', onlineDate='null', pubDate='1787846400000', pubDateStr='2026-08-28', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1790734425497, creator='13701087609', updateTime=1790739498146, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1312019807097160415, tenantId=1146029695717560320, journalId=1311385891987619962, issueId=1311998530802250506, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1312019807097160416, tenantId=1146029695717560320, journalId=1311385891987619962, issueId=1311998530802250506, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=806, endPage=816, ext={EN=ArticleExt(id=1311999380450795556, articleId=1311999380052336675, tenantId=1146029695717560320, journalId=1311385891987619962, language=EN, title=Fractal characteristics of karst geology in large-scale thrust-nappe tectonic settings, columnId=1311998890077938361, journalTitle=Journal of Geomechanics, columnName=Tectonic System & Structural Geology, runingTitle=null, highlight=null, articleAbstract=
Objective

Large-scale thrust-nappe structures have a significant impact on the regional geological environment and are important factors controlling the development of karst systems. Quantitative analysis of karst geological fractal characteristics in such settings provides essential scientific insights into the nonlinear behavior of complex karst systems.

Methods

Focusing on the karst region along the Qingfeng fault zone, the box-counting dimension method of geological fractal theory was used to quantify key geological elements. We evaluated the fractal characteristics across both regional scales and watershed units to determine their fractal dimensions and scaling properties.

Results

The stratigraphic boundaries at both regional and watershed scales exhibit pronounced fractal characteristics. Karstification significantly enhances boundary complexity, leading to higher fractal dimensions in areas with more advanced karst development. Furthermore, thrust-nappe structures and tectonic movements strongly influence drainage network fractals, modifying the conventional spatial mapping between surface and groundwater systems. The fractal dimensions of surface drainage systems show a positive correlation with those of subsurface karst drainage systems. Peak landforms in the study area exhibit youth-stage peak-cluster characteristics, indicating an early stage in the regional karst geomorphic cycle.

Conclusions

Karst in the region exhibits fractal characteristics, and the peak evolution follows the three-stage patterns common in karst areas. Surface and groundwater systems have positively correlated fractal patterns, and stratigraphic boundary dimensions serve as a robust indicator of karst development intensity.

Significance

Clarifying the self-similarity of karst in thrust-nappe tectonic zones provides a quantitative reference and theoretical basis for assessing the relationships between faulting, karst distribution, and evolutionary dynamics, offering a valuable methodological approach for addressing similar karst geological issues.

, authors=Xiaodi SHI, Jianxin YAO, Biyi ZHAO, Dan YAO, Li KUANG, authorsList=Xiaodi SHI, Jianxin YAO, Biyi ZHAO, Dan YAO, Li KUANG, authorCompany=null, correspAuthors=Jianxin YAO, authorNote=null, correspAuthorsNote=null, copyrightStatement=Copyright ©2026 Journal of Geomechanics. All rights reserved., copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1311999393415389264, articleId=1311999380052336675, tenantId=1146029695717560320, journalId=1311385891987619962, language=CN, title=大型逆冲推覆构造地质背景下喀斯特地质分形特征, columnId=1311998893139780288, journalTitle=地质力学学报, columnName=构造体系与构造地质, runingTitle=null, highlight=null, articleAbstract=

大型逆冲推覆构造对区域地质环境具有显著影响,是控制喀斯特体系发育的重要因素。探究在此背景下的喀斯特地质分形特征,能够为分析复杂喀斯特系统非线性问题提供科学依据。以青峰大断裂喀斯特区为研究对象,采用地质分形理论盒维数法量化区内各典型要素,探讨区域要素及流域单元要素分形特征,确定各典型要素分维值及分形特征。研究结果表明:区域和流域单元地层线均具有明显分形特征,喀斯特化进程对地层线具有明显的增维作用,喀斯特越发育,分维值越大;同时逆冲推覆构造及构造运动对水系分形特征影响较大,会改变地表水系与地下水系的一般映射关系,地表水系分维值与地下喀斯特水系统分维值呈现近似正相关规律。青峰断裂带喀斯特区峰体表现为幼年期峰丛地貌,表明其现处于喀斯特旋回发育的早期。区内喀斯特具有分形特征,峰体演化遵循一般喀斯特区的三段式演化规律,地表水系与地下水系表现出正相关的分形规律,地层线分维值对喀斯特发育程度具有明显的指示意义。明确逆冲推覆构造区的喀斯特自相似性,可为研究断裂构造与喀斯特分布、发育程度及演化规律提供定量化分析的参考和理论依据,也为解决同类地区中喀斯特地质问题提供了新思路。

, authors=史箫笛, 姚建新, 赵碧义, 姚丹, 况丽, authorsList=史箫笛, 姚建新, 赵碧义, 姚丹, 况丽, authorCompany=null, correspAuthors=姚建新, authorNote=

作者贡献声明

史箫笛、姚建新负责论文构思、数据分析、研究方法和论文写作;史箫笛、姚建新、赵碧义参与数据分析和技术手段的实践应用和绘图;史箫笛、姚丹、况丽参与数据分析、研究方法和修改。所有作者均阅读并同意稿件的提交和发表。

Author’s Contributions

SHI Xiaodi and YAO Jianxin conceived the study, performed data analysis, designed the research methodology, and drafted the manuscript; SHI Xiaodi, YAO Jianxin, and ZHAO Biyi participated in data analysis, practical application of technical approaches, and figure generation; SHI Xiaodi, YAO Dan and KUANG Li were involved in data analysis, refinement of the research methodology, and manuscript revision. All authors have read and approved the submission and publication of the manuscript.

史箫笛(1994—),男,硕士,工程师,主要从事水文地质、工程地质方面工作。Email:

, correspAuthorsNote=
姚建新(1976—),男,高级工程师,主要从事水文与工程地质勘察、设计和基础工程施工方面工作。Email:
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language=CN, orderNo=3, keyword=分维值), Keyword(id=1311999407629885562, tenantId=1146029695717560320, journalId=1311385891987619962, articleId=1311999380052336675, language=CN, orderNo=4, keyword=增维), Keyword(id=1311999407730548859, tenantId=1146029695717560320, journalId=1311385891987619962, articleId=1311999380052336675, language=CN, orderNo=5, keyword=分形特征)], refs=[Reference(id=1311999419604623508, tenantId=1146029695717560320, journalId=1311385891987619962, articleId=1311999380052336675, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=1, rfOrder=0, authorNames=null, journalName=null, refType=null, unstructuredReference=CHEN L, 2009. 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unstructuredReference=张满仓, 兰天伟, 贾伟东, 等, 2023. 断裂构造分形几何特征对冲击地压的控制作用研究[J]. 煤炭工程, 55(5): 103-110., articleTitle=null, refAbstract=null), Reference(id=1311999438239916266, tenantId=1146029695717560320, journalId=1311385891987619962, articleId=1311999380052336675, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=79, rfOrder=78, authorNames=null, journalName=null, refType=null, unstructuredReference=张元, 王红岩, 李育, 等, 2024. 西秦岭夏河-合作地区断裂构造分形结构特征及成矿预测[J]. 矿床地质, 43(2): 359-372., articleTitle=null, refAbstract=null), Reference(id=1311999438332190955, tenantId=1146029695717560320, journalId=1311385891987619962, articleId=1311999380052336675, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=80, rfOrder=79, authorNames=null, journalName=null, refType=null, unstructuredReference=赵海军, 张家祥, 彭昊, 等, 2025. 考虑参数不确定性的强震区危岩崩塌运动规律分析[J]. 工程地质学报, 33(1): 224-239., articleTitle=null, refAbstract=null), Reference(id=1311999438659346668, tenantId=1146029695717560320, journalId=1311385891987619962, articleId=1311999380052336675, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=81, rfOrder=80, authorNames=null, journalName=null, refType=null, unstructuredReference=周宁, 刘波, 2009. 鄂西南岩溶地区表层岩溶带发育强度变化规律研究[J]. 中国岩溶, 28(1): 1-6., articleTitle=null, refAbstract=null), Reference(id=1311999438730649837, tenantId=1146029695717560320, journalId=1311385891987619962, articleId=1311999380052336675, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=82, rfOrder=81, authorNames=null, journalName=null, refType=null, unstructuredReference=朱晓华, 王建, 陆娟, 2001. 关于地学中分形理论应用的思考[J]. 南京师大学报(自然科学版), 24(3): 93-98., articleTitle=null, refAbstract=null), Reference(id=1311999438793564398, tenantId=1146029695717560320, journalId=1311385891987619962, articleId=1311999380052336675, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=83, rfOrder=82, authorNames=null, journalName=null, refType=null, unstructuredReference=朱晓华, 蔡运龙, 2003. 中国水系的盒维数及其关系[J]. 水科学进展, 14(6): 731-735., articleTitle=null, refAbstract=null), Reference(id=1311999439078777071, tenantId=1146029695717560320, journalId=1311385891987619962, articleId=1311999380052336675, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=84, rfOrder=83, authorNames=null, journalName=null, refType=null, unstructuredReference=邹明清, 2007. 分形理论的若干应用[D]. 武汉: 华中科技大学., articleTitle=null, refAbstract=null)], funds=null, companyList=[AuthorCompany(id=1311999396053606482, tenantId=1146029695717560320, journalId=1311385891987619962, articleId=1311999380052336675, xref=null, 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articleId=1311999380052336675, language=EN, label=Fig.3, caption=Linear regression fit for the Gaozu River drainage system, figureFileSmall=UtWYRjf1JvdQgDbSxTd5AA==, figureFileBig=NA2eDk8wEAL5Ue16ENN5tw==, tableContent=null), ArticleFig(id=1311999411492839553, tenantId=1146029695717560320, journalId=1311385891987619962, articleId=1311999380052336675, language=CN, label=图3, caption=水系(高祖河)线性回归曲线

r—网格边长;$ N\left(r\right) $—盒子数

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a—喀斯特化阶段与峰体形态示意图;b—喀斯特化阶段峰体曲线示意图

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Fractal grid counts of the Gaozu River drainage system

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方形网边长r网格数$ N\left(r\right) $ $ \lg r $ $ \lg N\left(r\right) $
500 m192.69901.2788
300 m342.47711.5315
200 m502.30101.6990
150 m672.17611.8261
100 m1032.00002.0128
80 m1311.90312.1173
50 m2091.69902.3201
30 m3501.47712.5441
), ArticleFig(id=1311999415611646091, tenantId=1146029695717560320, journalId=1311385891987619962, articleId=1311999380052336675, language=CN, label=表1, caption=

水系(高祖河)分形网格数

, figureFileSmall=null, figureFileBig=null, tableContent=
方形网边长r网格数$ N\left(r\right) $ $ \lg r $ $ \lg N\left(r\right) $
500 m192.69901.2788
300 m342.47711.5315
200 m502.30101.6990
150 m672.17611.8261
100 m1032.00002.0128
80 m1311.90312.1173
50 m2091.69902.3201
30 m3501.47712.5441
), ArticleFig(id=1311999416039465100, tenantId=1146029695717560320, journalId=1311385891987619962, articleId=1311999380052336675, language=EN, label=Tab.2, caption=

Fractal characteristics of regional drainage systems

, figureFileSmall=null, figureFileBig=null, tableContent=
方形网
边长(r)/m
500300200150100805030分维值
水系名称网格数$ N\left(r\right) $
高祖河193450671031312093501.0311
泉河38721061432212874467391.0473
石甸河81422284250851340.9956
五石道河345691119300.8382
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区域水系分形特征

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方形网
边长(r)/m
500300200150100805030分维值
水系名称网格数$ N\left(r\right) $
高祖河193450671031312093501.0311
泉河38721061432212874467391.0473
石甸河81422284250851340.9956
五石道河345691119300.8382
), ArticleFig(id=1311999417276784782, tenantId=1146029695717560320, journalId=1311385891987619962, articleId=1311999380052336675, language=EN, label=Tab.3, caption=

Fractal characteristics of regional stratigraphic boundaries

, figureFileSmall=null, figureFileBig=null, tableContent=
地层代号喀斯特层组方形网边长(r)/m500300200150100805030分维值喀斯特发育程度
岩性网格数N(r)
Є2qn夹层状碳酸盐岩泥质白云岩101522294352831380.9399弱
Є1t夹层状碳酸盐岩灰岩111520284355891490.9589弱
Є1sl纯层碳酸盐岩灰岩119222352472706882141023501.0475强
Є1s间互状碳酸盐岩灰岩9015123131647659795315911.0137中等
Z2dn纯层碳酸盐岩白云岩4360931231842313666091.0242强
), ArticleFig(id=1311999417360670863, tenantId=1146029695717560320, journalId=1311385891987619962, articleId=1311999380052336675, language=CN, label=表3, caption=

区域地层线分形特征

, figureFileSmall=null, figureFileBig=null, tableContent=
地层代号喀斯特层组方形网边长(r)/m500300200150100805030分维值喀斯特发育程度
岩性网格数N(r)
Є2qn夹层状碳酸盐岩泥质白云岩101522294352831380.9399弱
Є1t夹层状碳酸盐岩灰岩111520284355891490.9589弱
Є1sl纯层碳酸盐岩灰岩119222352472706882141023501.0475强
Є1s间互状碳酸盐岩灰岩9015123131647659795315911.0137中等
Z2dn纯层碳酸盐岩白云岩4360931231842313666091.0242强
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Fractal characteristics of stratigraphic boundaries in watershed units

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单元编号分维值单元
编号
分维值单元
编号
分维值单元
编号
分维值单元
编号
分维值单元
编号
分维值单元
编号
分维值
“/”表示该单元内无地层线
10.852316/31/461.0115610.7553760.8496910.7503
20.881417/320.7664470.8873620.850677920.7583
30.9111180.8437330.9520480.837963/780.917093/
4/19/340.861349/640.8916790.8753940.8836
5/20/350.922050/65/800.888995/
60.883421/36/510.8726660.9040811.026796/
7/220.9220370.9329520.8814670.8287820.8922970.9018
80.937923/38/530.7356680.9450830.780598/
9/24/39/540.834469/840.9225990.8691
100.9144250.9502400.8646550.912770/850.9992100/
11/26/410.9161560.940171/86/1010.8053
12/270.917442/570.7369720.908587/1020.7801
13/280.8994430.9149580.8287730.9776880.8860103/
140.9825290.9613440.8414590.7533740.883689/
150.734230/45/600.7426750.8048901.0814
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流域单元地层线分形特征

, figureFileSmall=null, figureFileBig=null, tableContent=
单元编号分维值单元
编号
分维值单元
编号
分维值单元
编号
分维值单元
编号
分维值单元
编号
分维值单元
编号
分维值
“/”表示该单元内无地层线
10.852316/31/461.0115610.7553760.8496910.7503
20.881417/320.7664470.8873620.850677920.7583
30.9111180.8437330.9520480.837963/780.917093/
4/19/340.861349/640.8916790.8753940.8836
5/20/350.922050/65/800.888995/
60.883421/36/510.8726660.9040811.026796/
7/220.9220370.9329520.8814670.8287820.8922970.9018
80.937923/38/530.7356680.9450830.780598/
9/24/39/540.834469/840.9225990.8691
100.9144250.9502400.8646550.912770/850.9992100/
11/26/410.9161560.940171/86/1010.8053
12/270.917442/570.7369720.908587/1020.7801
13/280.8994430.9149580.8287730.9776880.8860103/
140.9825290.9613440.8414590.7533740.883689/
150.734230/45/600.7426750.8048901.0814
), ArticleFig(id=1311999417863987346, tenantId=1146029695717560320, journalId=1311385891987619962, articleId=1311999380052336675, language=EN, label=Tab.5, caption=

Fractal characteristics of stratigraphic boundaries in regional watershed units

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级次分形特征地层代号
Є2qnЄ1tЄ1slЄ1sZ2dn
流域单元分维值0.81700.85890.90080.86070.8954
区域单元0.93990.95891.04751.01371.0242
), ArticleFig(id=1311999419482988691, tenantId=1146029695717560320, journalId=1311385891987619962, articleId=1311999380052336675, language=CN, label=表5, caption=

区域−流域单元各地层线分形特征

, figureFileSmall=null, figureFileBig=null, tableContent=
级次分形特征地层代号
Є2qnЄ1tЄ1slЄ1sZ2dn
流域单元分维值0.81700.85890.90080.86070.8954
区域单元0.93990.95891.04751.01371.0242
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大型逆冲推覆构造地质背景下喀斯特地质分形特征
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史箫笛 , 姚建新 , 赵碧义 , 姚丹 , 况丽
地质力学学报 | 构造体系与构造地质 2026,32(4): 806-816
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地质力学学报 |构造体系与构造地质 2026 , 32 (4) : 806 -816
大型逆冲推覆构造地质背景下喀斯特地质分形特征
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史箫笛 , 姚建新 , 赵碧义, 姚丹, 况丽
作者信息
  • 湖北省地质局第八地质大队,湖北 襄阳 441000
通讯作者:
姚建新(1976—),男,高级工程师,主要从事水文与工程地质勘察、设计和基础工程施工方面工作。Email:
作者简介:

作者贡献声明

史箫笛、姚建新负责论文构思、数据分析、研究方法和论文写作;史箫笛、姚建新、赵碧义参与数据分析和技术手段的实践应用和绘图;史箫笛、姚丹、况丽参与数据分析、研究方法和修改。所有作者均阅读并同意稿件的提交和发表。

Author’s Contributions

SHI Xiaodi and YAO Jianxin conceived the study, performed data analysis, designed the research methodology, and drafted the manuscript; SHI Xiaodi, YAO Jianxin, and ZHAO Biyi participated in data analysis, practical application of technical approaches, and figure generation; SHI Xiaodi, YAO Dan and KUANG Li were involved in data analysis, refinement of the research methodology, and manuscript revision. All authors have read and approved the submission and publication of the manuscript.

史箫笛(1994—),男,硕士,工程师,主要从事水文地质、工程地质方面工作。Email:

Fractal characteristics of karst geology in large-scale thrust-nappe tectonic settings
Xiaodi SHI , Jianxin YAO , Biyi ZHAO, Dan YAO, Li KUANG
Affiliations
  • The Eighth Geological Brigade of Hubei Provincial Geological Bureau, Xiangyang 441000, Hubei, China
出版时间: 2026-08-28 doi: 10.12090/j.issn.1006-6616.2025039
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大型逆冲推覆构造对区域地质环境具有显著影响,是控制喀斯特体系发育的重要因素。探究在此背景下的喀斯特地质分形特征,能够为分析复杂喀斯特系统非线性问题提供科学依据。以青峰大断裂喀斯特区为研究对象,采用地质分形理论盒维数法量化区内各典型要素,探讨区域要素及流域单元要素分形特征,确定各典型要素分维值及分形特征。研究结果表明:区域和流域单元地层线均具有明显分形特征,喀斯特化进程对地层线具有明显的增维作用,喀斯特越发育,分维值越大;同时逆冲推覆构造及构造运动对水系分形特征影响较大,会改变地表水系与地下水系的一般映射关系,地表水系分维值与地下喀斯特水系统分维值呈现近似正相关规律。青峰断裂带喀斯特区峰体表现为幼年期峰丛地貌,表明其现处于喀斯特旋回发育的早期。区内喀斯特具有分形特征,峰体演化遵循一般喀斯特区的三段式演化规律,地表水系与地下水系表现出正相关的分形规律,地层线分维值对喀斯特发育程度具有明显的指示意义。明确逆冲推覆构造区的喀斯特自相似性,可为研究断裂构造与喀斯特分布、发育程度及演化规律提供定量化分析的参考和理论依据,也为解决同类地区中喀斯特地质问题提供了新思路。

逆冲推覆构造  /  喀斯特  /  分维值  /  增维  /  分形特征
Objective

Large-scale thrust-nappe structures have a significant impact on the regional geological environment and are important factors controlling the development of karst systems. Quantitative analysis of karst geological fractal characteristics in such settings provides essential scientific insights into the nonlinear behavior of complex karst systems.

Methods

Focusing on the karst region along the Qingfeng fault zone, the box-counting dimension method of geological fractal theory was used to quantify key geological elements. We evaluated the fractal characteristics across both regional scales and watershed units to determine their fractal dimensions and scaling properties.

Results

The stratigraphic boundaries at both regional and watershed scales exhibit pronounced fractal characteristics. Karstification significantly enhances boundary complexity, leading to higher fractal dimensions in areas with more advanced karst development. Furthermore, thrust-nappe structures and tectonic movements strongly influence drainage network fractals, modifying the conventional spatial mapping between surface and groundwater systems. The fractal dimensions of surface drainage systems show a positive correlation with those of subsurface karst drainage systems. Peak landforms in the study area exhibit youth-stage peak-cluster characteristics, indicating an early stage in the regional karst geomorphic cycle.

Conclusions

Karst in the region exhibits fractal characteristics, and the peak evolution follows the three-stage patterns common in karst areas. Surface and groundwater systems have positively correlated fractal patterns, and stratigraphic boundary dimensions serve as a robust indicator of karst development intensity.

Significance

Clarifying the self-similarity of karst in thrust-nappe tectonic zones provides a quantitative reference and theoretical basis for assessing the relationships between faulting, karst distribution, and evolutionary dynamics, offering a valuable methodological approach for addressing similar karst geological issues.

thrust-nappe structures  /  karst  /  fractal dimension  /  dimension enhancement  /  fractal characteristics
史箫笛, 姚建新, 赵碧义, 姚丹, 况丽. 大型逆冲推覆构造地质背景下喀斯特地质分形特征. 地质力学学报, 2026 , 32 (4) : 806 -816 . DOI: 10.12090/j.issn.1006-6616.2025039
Xiaodi SHI, Jianxin YAO, Biyi ZHAO, Dan YAO, Li KUANG. Fractal characteristics of karst geology in large-scale thrust-nappe tectonic settings[J]. Journal of Geomechanics, 2026 , 32 (4) : 806 -816 . DOI: 10.12090/j.issn.1006-6616.2025039
1967年美国数学家曼德布罗特提出了分形概念,并于1975年开创了分形几何学,成为研究各种复杂对象的有利工具(Mandelbrot,1975)。自然界的许多物理现象并不是有序、稳定和确定性的,而是无序、不稳定和随机的,其发生与发展并不是线性的,因此难以用传统数学诸如微分、函数等描述其过程与结果,而分形理论通过研究复杂系统的自相似性(申维和赵鹏大,1998;朱晓华等,2001;李苍松,2006;张佳瑞等,2017),揭示非线性系统中有序与无序的统一、确定性与随机性的统一,并得出隐藏在复杂现象背后的规律及局部和整体之间的本质联系。
分形理论已被广泛应用于海岸地貌、喀斯特地貌、流水地貌、冰川冻土、沙漠化、岩石结构演化及构造地质等地学领域中(秦耀辰和刘凯,2003;高义等,2011;文力等,2020;侯圣山等,2024)。在喀斯特地质学领域,运用分形理论计算构成喀斯特形态系统的峰体、洼地、洞穴系统及水文网的分维值,可揭示分维的喀斯特学含义,从喀斯特系统介质场结构及喀斯特作用过程的非线性动力特征分析其形态系统的分形机理(胡章喜和沈继方,1994;许模等,2011)。李苍松等(2017)研究认为喀斯特地下水化学特征参数仍具有分形特征,溶蚀实验水化学分形评价指数与偏光显微镜实验微观喀斯特分形指数之间显著相关,并通过水化学动力学−分形指数综合分维值评价了喀斯特发育程度。在构造地质领域中,中国大陆壳体中深大断裂的分布具有分形结构特征,大陆全境的分维值为1.493,各构造区的分维值为0.827~1.624,构造活动区分维值显著大于稳定区(谭凯旋等,1998)。同时发育于构造活动强烈的较浅部脆性、张扭性断裂带分维值较大,发育于构造活动较弱地区的深部韧性、剪切断裂带分维值较小(成永生,2010)。区域上断裂构造分形维数值能够反映地层能干性及构造应力的传递过程,指示逆冲推覆过程中主应力面作用方向(姜颜良等,2023)。分形理论也被应用于油气藏、矿产及灾害地质领域。储层孔隙结构是油气储能的关键因素,在页岩储层微观研究中通过分形维数这一标度参数可有效描述孔隙表面的粗糙度与孔隙结构的复杂程度,为页岩储集与空间评价提供理论基础(李琦等,2025;李帅智等,2025)。构造活动与成矿作用存在密切的时空及成因联系,断裂容量维高值区构造复杂,连通性较好,能保证成矿流体远距离流动,利于成矿;断裂容量维低值区构造简单,能圈闭住成矿流体,为高值区输送来的成矿流体沉积提供壁垒(张元等,2024)。利用分形理论也能够实现坡面形态特征的随机模拟,为危岩崩塌落石运动坡面细观形态难以准确建模及定量表征的问题提供了解决方法(赵海军等,2025)。
喀斯特发育主要受控于岩性、构造及水动力条件等因素,各因素不断相互叠加与转化造成了喀斯特系统的复杂性,传统经典数学方法难以定量刻画喀斯特系统复杂的空间结构。各种喀斯特形态是其内部系统的外在体现,而分形理论能够通过研究地表喀斯特形态来定量描述和刻画其内部系统结构,通过分析喀斯特地貌分形特征、喀斯特区水文网分形特征、喀斯特裂隙及洞穴分形特征、喀斯特水化学分形特征等,可揭示喀斯特系统内部特征及量化其发育程度(高伟等,2016;李苍松等,2017)。在大型逆冲推覆构造地质背景下,采用分形理论定量分析喀斯特的自相似性及分形特征,量化喀斯特发育规律及程度,对山区隧道等地下洞室的围岩稳定、涌突水问题及道桥工程建设中基础稳定性具有重要意义。
青峰−襄樊(襄阳)−广济断裂是分隔秦岭造山带和扬子克拉通2个一级构造单元的区域性大断裂,其中襄樊(襄阳)以西称为青峰大断裂,经多期构造作用叠加,构造形迹十分复杂。北大巴山逆冲−褶皱带以低角度平缓地向南逆掩于扬子克拉通的边缘之上,两侧发育与主断裂近似平行向北缓倾的多条长度不一的次级逆冲断裂(陈璘,2009;王志元等,2014;张国伟等,2019)。以青峰大断裂为界,可划分为北大巴山逆冲推覆构造带和南大巴山前陆构造带。南大巴山前陆构造带又可分为北部前陆褶冲带及南部前陆褶皱带(董云鹏等,2008)。北大巴山逆冲推覆构造带发育韧性剪切带、紧闭褶皱及糜棱岩化,变形强度大。南大巴山前陆构造带以冲断−褶皱变形为主,自北向南进一步分为叠瓦冲断带、冲断褶皱带、逆冲推覆扩展褶皱带及低缓褶皱带,变形强度递减,褶皱由紧闭渐变为宽缓箱状。研究区位于丰溪镇中部地区,属前陆褶冲带,以冲断变形为主,形成一系列叠瓦式逆冲断裂构造。区内青峰大断裂主要由主断裂(F1)及5条次级(F2—F6)断裂组成,构成叠瓦式冲断系统。其中主断裂西起陕鄂边界西米河村,东至丰溪镇辽叶村,绵延超过20 km,走向由北东向在丰溪镇下坝村附近渐变为东西向;5条次级断裂近东西向展布,以青峰主断裂为界,北部为震旦系耀岭河组(Z1yl)板岩,南部为寒武系灰岩组、震旦系白云岩组。南部也是研究的主要区域。
丰溪镇中部地区碳酸盐岩广泛分布(图1),主要包括寒武系石龙洞组(Є1sl)灰岩、天河板组(Є1t)灰岩、水井沱组(Є1s)灰岩及覃家庙组(Є2qn)泥质白云岩及震旦系灯影组(Z2dn)白云岩。根据岩性及沉积构造特征可划分为纯层状碳酸盐岩类、间互状碳酸盐岩类及夹层状碳酸盐岩类3大类。石龙洞组(Є1sl)灰岩及灯影组(Z2dn)白云岩属纯层状碳酸盐岩类,多为厚层—巨厚层构造,地层均匀且连续性较好,喀斯特强烈发育;水井沱组(Є1s)灰岩属间互状碳酸盐岩类,表现为可溶岩与非可溶岩交替沉积出现,喀斯特中等发育;天河板组(Є1t)灰岩、覃家庙组(Є2qn)泥质白云岩属夹层状碳酸盐岩类,表现为非可溶岩中夹有可溶岩,可溶岩呈夹层状产出,喀斯特弱发育。从地貌上来看(图2),周家坝村、纸坊村、庙子沟及辽叶湖一带发育有溶蚀盆地、溶蚀平原及峰丛谷地,洼地、落水洞、溶洞及暗河等喀斯特地貌个体形态种类齐全,但溶蚀发育规模、溶蚀深度均弱于鄂西典型喀斯特山区(王增银等,1995;周宁和刘波,2009;史箫笛等,2023)。
分形理论能够量化断裂系统与喀斯特系统的复杂程度,分维值是分形理论的定量化标准和基本参数。现已演化出多种计算方法,如相似维数、盒维数、信息维数、关联维数、Lyapunov维等,在构造地质学、喀斯特地质学中应用最为广泛的是盒维数与信息维数(邹明清,2007;许模等,2011;张元等,2024)。其中盒维数法能够高效降低多维数据,适用于多尺度及地质复杂结构,故研究采用盒维数法进行计算。盒维数法通常采用不同边长的二维正交网格(盒子)覆盖研究区,统计包含目标要素的盒子数量,将网格边长与盒子数在对数坐标系中进行回归分析。若其存在良好的线性关系,则说明分形几何结构明显,回归直线的斜率即为分维值。假设网格边长为r,盒子数为$ N\left(r\right) $,则满足如下函数关系(胡章喜和沈继方,1994;张飞燕和陈晓山,2008;张满仓等,2023;王榕臻等,2024):
$ N\left(r\right)={C}_{1}{r}^{-{{D}_{1}}} $
对统计结果在双对数坐标中进行回归分析,拟合曲线为一条直线,则满足线性回归方程:
$ \lg N\left(r\right)=-D \lg r+C $
式中,r—网格边长;$ N\left(r\right) $—盒子数;C、C1—常数;D、D1—分维值。
文章采用不同尺度进行分形特征研究,即区域大尺度和流域单元小尺度,试图揭示从宏观到微观自相似的递归迭代规律。不同尺度上的计算方法相同,均按照不同大小的方形网格去覆盖水系及地层线等要素,各要素数据来源于中国地质调查局地质云平台1∶20万地质图(https://geocloud.cgs.gov.cn/)和1∶20万水文地质图(https://geocloud.cgs.gov.cn/);计算方形网格大小分别为30 m×30 m、50 m×50 m、80 m×80 m、100 m×100 m、150 m×150 m、200 m×200 m、300 m×300 m、500 m×500 m,通过统计分析$ \lg r $与$ \lg N\left(r\right) $之间的线性回归关系,得到各要素分维值。如对水系(高祖河)利用ArcGIS渔网工具将研究区划分不同大小的方形网格,再利用叠加分析功能,统计水系跨越的网格数(表1),经线性回归统计分析(图3),即可得出分维值1.0311,其余各要素分析方法相同。
区域上以水系及地层线要素整体为研究对象,量化各要素空间结构的自相似性及复杂性,构建空间分析的统一框架。流域作为一个相对独立的单元,通过水流的作用与周围区域进行物质和能量交换。流域单元是水文循环与喀斯特作用的空间载体,遵循补给−径流−排泄的动态平衡,具有层级嵌套结构,地表水文过程与地下喀斯特地质结构的空间耦合构成完整的水资源循环单元(Han and Zhou,1996;蒙海花和王腊春,2010;吴乔枫等,2017)。流域单元与喀斯特作用的关系表现为流域边界控制喀斯特发育空间格局,水文过程作为喀斯特水动力场驱动溶蚀效应。喀斯特作用正是基于这样的单元而不断发展的,因此将丰溪镇中部地区划分为一定数量的流域单元,探究地层线在各单元内的分形特征及其与喀斯特的关系。底图采用ALOS(Advanced Land Observing Satellite)卫星相控阵型L波段合成孔径雷达采集的12.5 m分辨率数字高程模型(DEM),利用ArcGIS水文分析工具,将丰溪镇中部地区划分为103个流域单元(图4),仍按照上述不同大小方格网去覆盖地层线要素,并统计分析$ \lg r $与$ \lg N\left(r\right) $之间的线性回归关系,得到流域单元内要素分维值。
树枝状的河流包括干流及支流在内的河网体系,其本身就具有自相似性,其分维值的大小反映了水系的发育程度及流域地貌的侵蚀发育程度。区内水系属堵河水系,堵河为汉江第一大支流,而汉江为长江的第一大支流,长江流域水系分维值为1.3292(朱晓华和蔡运龙,2003)。区内水系分维值为0.8382~1.0473(表2),泉河作为区内最大河流,其分维值最大,反映出其发育及侵蚀程度更大,而其低于长江水系流域分维值正是随着河流级次降低分维值一般逐渐降低规律的体现。在喀斯特区,地表水系的形成既有流水侵蚀作用,也有流水溶蚀作用。地表水系与地下水系存在一定程度上的映射关系,通常地表水系强发育的地区,地下水系相对弱发育;而地表水系弱发育的地区,地下水系相对强发育。若按此规律,区内地表水系分维值较低,发育程度低,那地下水系将会强发育。但事实并非如此,地下仅零星分布规模不大的管道网络系统。由此可见,逆冲推覆构造及构造运动对水系的发育具有重要影响,会改变这种映射的相对关系。区内断裂构造控制地表河流形态分布与流向,局部断裂错断导致水系错动(雷东宁等,2012),诱发水系重组;而断裂上下盘的导水差异性及断裂形成的裂隙网络介质塑造了地下水系的基本分布格局。更新世以来的构造运动则通过抬升作用改变了分水岭位置,引发河流袭夺(李俊涛和张毅,2007);抬升作用也造成了侵蚀基准面下降,改变了原有的补给−排泄条件,进一步影响地下水系的发育(王增银等,1995)。映射关系的异化正是两者协同作用的结果,这种关系反映了地表水系统向地下水系统的独特转化过程。就常流水系而言,喀斯特区地表水系的分支结构仍具有自相似性,且一般地表水系分维值大于地下水系分维值。如贵州喀斯特流域地表水系分维值为1.16~1.64,而地下水系分维值为1.11~1.27(梁虹和卢娟,1997)。与之表现不同的是区内地表水系分维值普遍更低,推测地下水系分维值更甚之,故未形成大规模地下河网系统。因此,就此逆冲推覆构造区而言,地表水系分维值与地下喀斯特水系统分维值并不符合呈负相关的一般规律,即不遵循地表水系分维数与喀斯特发育强度呈负相关,而是呈现出一种近似正相关的规律。
在喀斯特地貌分形特征研究中,等高线与喀斯特洼地等线状或面状形态最为常见。其具有自相似性,等高线分维值越大,喀斯特发育越强烈;而喀斯特洼地分维值越小,喀斯特发育越强烈(王迪等,2010;高伟等,2016)。等高线与喀斯特洼地的本质仍然是区域或局部可溶岩经溶蚀作用形成的空间分布不均的具有典型边界特征的溶蚀单元,因此文章仍然可以采用这种方法来研究地层线的分形特征。事实上,地层界线两侧岩性的可溶性差异是控制喀斯特发育的重要因素,可溶岩与非可溶岩或纯碳酸盐岩与不纯碳酸盐岩接触界面常形成喀斯特发育的边界条件,非可溶岩或不纯碳酸盐岩往往成为限制喀斯特地下水侧向运移边界或喀斯特地下水的排泄边界,边界带范围具备良好的水动力条件。这种岩性界面可导致喀斯特发育强度突变,形成明显的喀斯特分带,是平面上研究喀斯特发育程度的理想线性要素。区内覃家庙组(Є2qn)、天河板组(Є1t)、石龙洞组(Є1sl)、水井沱组(Є1s)、灯影组(Z2dn)地层线分维值分别为0.9399、0.9589、1.0475、1.0137、1.0242(表3)。其中石龙洞组(Є1sl)地层线分维值最大,该地层为纯灰岩,落水洞、溶洞及暗河管道等喀斯特个体形态均存在,喀斯特最为发育;而覃家庙组(Є2qn)地层线分维值最小,该地层为泥质白云岩,各类喀斯特个体形态稀少,地表及地下喀斯特相对最不发育。区内各地层喀斯特发育程度与分维值大小一一对应,分维值越大,喀斯特越发育,说明喀斯特对地层线具有明显的增维作用;反之,分维值越小,喀斯特越不发育。且纯灰岩组分维值高于纯白云岩组,地层线分维值对喀斯特发育程度具有明显的指示意义。
地表不同类型和规模的峰体形态是喀斯特发育的典型外在表现形式之一,峰丛、峰林及孤峰通常分别对应于幼年期、壮年期及老年期3个喀斯特化阶段(图5a)。幼年期的峰丛通常成簇突起,中下部相连,峰体高度参差不齐,数量众多;壮年期的峰林成群簇生,基部微微相连,各峰体相对散开,高度参差不齐,数量较多;而老年期的孤峰为孤立的石灰岩山峰,数量少,高度显著降低。
若以不同的高度标尺δ统计高度超过此标尺的峰体个数N(δ),并形成拟合曲线,幼年期峰体会出现“先缓再陡后缓”的曲线形式(图5b),壮年期峰林表现出较平缓下降的曲线形式,而老年期孤峰则呈先缓后陡降的曲线形式(王迪等,2010)。区内峰体个数随着高度标尺的增大,呈“先缓再陡后缓”的曲线形式(图6)。峰体表现为幼年期峰丛地貌,表明现处于喀斯特发育的早期。但区内地下仍发育规模不大的喀斯特管道系统,其更可能是壮年期喀斯特化的产物,或者说是区内喀斯特化阶段曾很可能达到过壮年期。因更新世以来强烈的构造抬升运动,原始溶蚀夷平面基本被完全改造,在未完成一个完整的喀斯特旋回基础上,转而开始下一个喀斯特旋回,而现今正处于该喀斯特旋回的早期。构造运动对区内峰体形态影响较大,并影响着地表喀斯特地貌形态,峰体分形特征能够横向上说明喀斯特发育的当前期次,但无法解释纵向上喀斯特发育的历史和期次问题。
区域地层线具有明显的分形特征,而流域单元地层线是否仍具有分形特征,尚不明确。区内流域单元内地层线分维值为0.7342~1.0814(表4),平均值为0.8843,低于区域地层线分维值平均值0.9868。但相较于区域地层线分维值,流域单元地层线分维值小于其最小值而高于其最大值,分维值分布区间范围较大,数据也较为离散。这也从侧面反映出喀斯特发育的空间不均匀性,即使是同一地层在不同区段(流域单元)也会因构造、地貌及水文地质条件的差异而导致喀斯特发育程度不尽相同。基于对区域及流域单元内各地层线的分类统计结果(表5),流域单元内各地层线分维均值较区域分维均值有明显降低,石龙洞组(Є1sl)、灯影组(Z2dn)、水井沱组(Є1s)、天河板组(Є1t)及覃家庙组(Є2qn)降维幅度分别为14%、12.6%、15.1%、10.4%、13.1%,平均降维幅度为13%,尤其以水井沱组(Є1s)间互状碳酸盐地层分维值降幅最大,反映出在空间上喀斯特发育程度变化更为离散,这与其间互状地层结构密切相关。各地层中,石龙洞组(Є1sl)地层线分维值最大,为0.9008,喀斯特最为发育;而覃家庙组(Є2qn)地层线分维值最小,为0.8170,喀斯特相对最不发育。该结果与区域上地层线分形特征表现出了良好的一致性,再次证明了喀斯特系统的自相似作用,说明流域单元内地层线仍具有分形特征。地层线在区域大尺度或局部小尺度下分维值可能存在差异,即同一地区不同大小尺度下分维值不同,但其反映的喀斯特作用内涵是一致的,满足自相似规律,也是喀斯特作用微观与宏观的统一。
大型逆冲推覆构造对区域地质环境的影响是显著的,构造也是控制喀斯特体系的重要因素。宏观上,喀斯特形态发育各异,但从喀斯特最小溶蚀单位开始,再到溶孔→溶隙→溶槽→溶洞→喀斯特暗河,不同级次喀斯特形态具有自相似性,又具有形态特征不变即标度不变性。改变观察尺度标度(李苍松等,2007),诸如现今观测的溶洞,其必然是由一个自相似的更小溶蚀单元逐步发育而成。喀斯特系统的物质结构背景具有多层次性,其由不同喀斯特层组、区域构造形成总体格局,局部岩性结构并不是单一不变的,不同区段空间组合不一。构造特征也是如此,诸如褶皱及断裂。区域褶皱及断裂中包含着许多次级褶皱和断裂,而次级断裂与褶皱又被更低级别的褶皱与断裂分割至肉眼可见的节理或至显微镜下可见的裂隙。随着观察尺度的不断缩小,总是相似重现,这也是喀斯特地质分形的本质。宏观上对喀斯特区水系、地层线等要素进行地质分形研究,其意义在于能够通过线性解来解决喀斯特系统的非线性问题,即通过地表宏观简单线性组合要素推测地下喀斯特发育情况,诸如地层线的分形特征对喀斯特发育程度的指示意义。近年来,喀斯特地质分形多集中于对喀斯特孔隙的微观研究(李苍松等,2018;武东强等,2021;谭谣等,2024),且具有宏观向微观转变的趋势。但不管微观还是宏观,都可以尝试找到这样一个尺度,在这一尺度上喀斯特的复杂性能够被分解成为一个或多个简单的线性组合,通过对线性结构的研究来分析和处理喀斯特系统的非线性问题。
(1)逆冲推覆构造及构造运动对地下水系的发育具有重要影响,甚至会改变地表水系与地下水系映射的一般规律,但水系仍具有分形特征。丰溪镇中部地区地表水系分维值为0.8382~1.0473,分维值随着河流级次降低而降低;同时地下水系分维值较地表水系分维值更低,难以形成大规模的地下河网系统,仅零星分布规模不大的管道网络系统。区内地表水系分维值与地下喀斯特水系统分维值并不呈现负相关的一般规律,而是呈现出一种近似正相关的规律。
(2)丰溪镇中部地区峰体个数随着高度标尺的增大,呈“先缓再陡后缓”的曲线形式。峰体表现为幼年期峰丛地貌,表明其现处于喀斯特发育的早期;但区内各类喀斯特个体形态更可能暗示其为壮年期喀斯特化的产物。这说明构造运动对区内峰体形态影响较大,构造抬升运动将原始溶蚀夷平面改造,而现今正处于喀斯特旋回的发育早期。
(3)区域上石龙洞组(Є1sl)地层线分维值最大,喀斯特也最为发育;而覃家庙组(Є2qn)地层线分维值最小,喀斯特最不发育。各地层喀斯特发育程度与分维值大小具有一致性,分维值越大,喀斯特越发育;而分维值越小,喀斯特越不发育,喀斯特化作用对地层线具有明显的增维作用。流域单元内地层线也具有明显的分形特征,但分维值大小较区域地层线分维值更为离散,反映出喀斯特发育的空间不均匀性;且流域单元内各地层线分维均值较区域有明显降低,平均降维幅度为13%。其中石龙洞组(Є1sl)地层线分维值最大,覃家庙组(Є2qn)地层线分维值最小。流域单元与区域上地层线分形特征一致,也证明了喀斯特系统在区域及局部的自相似作用,地层线分形特征对喀斯特发育程度具有明显的指示意义。

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2026年第32卷第4期
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doi: 10.12090/j.issn.1006-6616.2025039
  • 接收时间:2025-04-09
  • 首发时间:2026-09-30
  • 出版时间:2026-08-28
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  • 收稿日期:2025-04-09
  • 修回日期:2025-10-27
  • 录用日期:2025-11-24
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    湖北省地质局第八地质大队,湖北 襄阳 441000

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姚建新(1976—),男,高级工程师,主要从事水文与工程地质勘察、设计和基础工程施工方面工作。Email:
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2种不同金属材料的力学参数
科
Family
属数
Number of
genus
种数
Number of
species
占总种数比例
Percentage of
total species (%)
属
Genus
种数
Number of
species
占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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