Geotechnical and Geological Engineering

, Volume 37, Issue 1, pp 375–387 | Cite as

Application of the Cohesion Softening–Friction Softening and the Cohesion Softening–Friction Hardening Models of Rock Mass Behavior to Estimate the Specific Energy of TBM, Case Study: Amir–Kabir Water Conveyance Tunnel in Iran

  • Majid Mirahmadi
  • Mohsen Soleiman Dehkordi
Original Paper


The specific energy (SE) of an excavation is an important factor to consider in economic and technological investigations of mechanical excavation projects using a tunnel-boring machine (TBM). SE is defined as the energy consumed during excavation of per unit volume of rock mass, and it can be determined in real time from the data recording the performance of a TBM. Several experimental, empirical, and analytical methods have been developed to predict SE based on rock mass and machine parameters. In this study, a new empirical method is proposed to predict SE based on the strain energy ratio of rock mass (Ψ). This is defined as the ratio of the residual post peak strain energy to the stored pre peak strain energy of the rock mass. It depends on three important parameters, namely rock mass properties, intact rock parameters, and rock mass behavior models. In this study, to estimate the strain energy ratio of rock mass, two post peak rock mass behavior models—cohesion softening–friction softening (CSFS) and cohesion softening–friction hardening (CSFH)—were used. Based on actual data from the Amir–Kabir water conveyance tunnel project, the relationships between the SE of TBM and the strain energy ratio were investigated. Due to different rock mass qualities in the tunnel route, classification of rock mass according to Hoek and Brown’s proposal was carried out, and the correlation between the mentioned parameters in each class was studied. The results showed a direct relationship between the parameters, and the best relationships in poor and moderate rock mass (geological strength index [GSI] < 65) were obtained using the CSFS model to clarify the rock mass’s post peak behavior, while the CSFH model was highly applicable for estimating the SE of TBM using the strain energy ratio in good rock mass (GSI > 70) because of its ability to modify the brittle behavior of brittle rock mass.


Specific energy Strain energy ratio CSFS model CSFH model GSI Amir–kabir water conveyance tunnel 



The authors are indebted to all staff, including consulting engineers, contractors, and employers, especially Sahel Consulting Engineers (SCE), for providing us with data, as well as all individuals who helped to us to prepare this paper.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of GeologyPayam Noor UniversityTehranIran
  2. 2.Department of Civil Engineering, Bafgh BranchIslamic Azad UniversityBafghIran

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