A Progressive Framework for Delineating Homogeneous Domains in Complicated Fractured Rock Masses: A Case Study from the Xulong Dam Site, China

  • Jiewei Zhan
  • Yunming Pang
  • Jianping ChenEmail author
  • Chen Cao
  • Shengyuan Song
  • Xin Zhou
Original Paper


As components of natural geological bodies, rock masses generally experience long-term endogenic and exogenic geological processes. Since the composition and structure of rock masses generally vary from one domain to another, it is necessary to divide rock masses into several approximately homogeneous domains before developing rock engineering designs. A progressive framework that integrates geological, geotechnical and structural aspects was proposed to demarcate homogeneous domains. The proposed framework was applied to identify the homogeneous domains along three exploration tunnels at the Xulong dam site. The demarcation of geological domains was mainly done by means of thin-section examination of rock specimens and outcrop investigation. Field observations and P wave velocity tests were used to distinguish the changes in the geotechnical properties of rock masses caused by rock unloading and weathering. The crack tensor, which can synthetically consider the orientation, dimension and volume density of discontinuities, was introduced to determine the structural similarity of rock masses based on in situ measurable quantities. The results show that the crack tensor can effectively distinguish structural differences and exhibits better performance than conventional orientation-based methods. A major advantage of the proposed progressive framework is that it provides a quantitative, logical and reasonable framework to delineate homogeneous domains based on the comprehensive utilization of available field data in a logical sequence.


Homogeneous domain Geological domain Geotechnical domain Structural domain Crack tensor Fractured rock mass 

List of Symbols


Crack tensor


Volume density of discontinuities


Dimension of discontinuities


Maximum size of discontinuities


Unit vector normal to discontinuity surface


Component of n

E(n, r)

Density function to show the statistical distribution of n and r


Solid angle corresponding to the surface of a unit sphere


Volume of rock masses


Serial number of discontinuities


Number of discontinuities in V


Principal value of Fij


Kronecker’s delta

\(I_{1}^{\left( F \right)}\)

The first invariant of Fij


Anisotropy index of discontinuity networks


The nth moment of r


Symmetric, second-rank tensor depending only on E(n)


Trace length


The nth moment of t


Unit vector parallel to scanline


Number of discontinuities that intersect with the unit length scanline

\({\varvec{F}}_{ij}^{{\left( {\text{Left}} \right)}}\)

Crack tensor for a rock mass domain (Left side)

\({\varvec{F}}_{ij}^{{\left( {\text{Right}} \right)}}\)

Crack tensor for a rock mass domain (right side)

\(\Delta {\varvec{F}}_{ij}^{\left( E \right)}\)

Error tensor


Relative error


Correlation coefficient


Average of tensor elements


P wave velocity of rock mass



The authors gratefully acknowledge the support from the Key Project of NSFC-Yunnan Joint Fund (Grant No. U1702241), the State Key Program of National Natural Science Fund of China (Grant No. 41330636), the National Natural Science Fund of China (Grant No. 41702301) and the Opening Fund of SKLGP (Grant No. SKLGP2018K017). The authors would like to kindly acknowledge the editor and two anonymous reviewers for their comments and suggestions which helped a lot in making this paper better.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  • Jiewei Zhan
    • 1
  • Yunming Pang
    • 2
  • Jianping Chen
    • 1
    Email author
  • Chen Cao
    • 1
  • Shengyuan Song
    • 1
    • 3
  • Xin Zhou
    • 1
  1. 1.College of Construction EngineeringJilin UniversityChangchunChina
  2. 2.Three Gorges Geotechnical Consultants Co., LtdWuhanChina
  3. 3.The State Key Laboratory of Geohazards Prevention and Geoenvironment Protection (SKLGP)Chengdu University of TechnologyChengduChina

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