Advances and Challenges in Multiple Failure State Triaxial Testing of Rocks – 50 years’ experience

Samad Narimani; Morteza Davarpanah; Balazs Vasarhelyi

doi:10.68732/1b40aab18156e52c

Paper contribution

Advances and Challenges in Multiple Failure State Triaxial Testing of Rocks – 50 years’ experience

Samad Narimani; Morteza Davarpanah; Balazs Vasarhelyi

DOI: https://doi.org/10.68732/1b40aab18156e52c
Proceedings: EUROCK 2026
Pages: 397-402
Submitted: 28 January 2026
Accepted: 15 June 2026
Published: 12 August 2026

Summary

Abstract

The Multiple Failure State (MFS) triaxial test enables several failure points to be obtained from a single specimen through successive loading under increasing confinement, offering substantial time and material savings over conventional tests. Since its introduction by Kovári and Tisa for 50 years ago, numerous modifications—such as the Continuous Failure State (CFS) and strain- or volume-controlled variants—have been developed to enhance test reliability. Despite its efficiency, the method’s applicability to brittle rocks remains debated due to cumulative damage and strain localization effects. This paper reviews fifty years of research on MFS testing, summarizing theoretical foundations, experimental progress, and comparisons with single-stage triaxial tests. The review identifies key parameters influencing test validity and provides recommendations for improving measurement accuracy and reproducibility in modern rock mechanics laboratories.

Contributors

Authors

Samad Narimani Budapest University of Technology and Economics ORCID 0000-0002-7779-9506
Morteza Davarpanah Institut de Recherche en Mines et en Environnement (IRME), Rouyn-Noranda, Canada ORCID 0000-0002-8046-5814
Balazs Vasarhelyi Budapest University of Technology and Economics ORCID 0000-0002-0568-1031

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Works cited

References

MFS/CFS variant/method notes
Main difference vs SST (qualitative)/reported bias
Kovári and Tisa, (1975)
Original Multiple Failure State and Strain-Controlled concepts; theoretical and early lab demonstration
Introduces concept: derive multiple failure points from one specimen; emphasizes instrumentation and stopping rules.
Kovári, et al. (1983)
Continuous failure state / steady stress-path control; theoretical/procedural paper
CFS maintains specimen at failure while changing stress path to trace envelope.
Crawford and Wylie (1987)
Modified MFS variants for reservoir cores — staged confining increases
Used successfully for reservoir cores where sample availability limited; stresses that corrections and careful control required.
Pagoulatos (2004)
MFS variants; volumetric inflection / ΔV/V stopping criteria
Generally close agreement for Berea sandstone with careful stopping rules; differences depend on stopping criterion (authors analyze sensitivity).
Youn&Tonon, (2010)
“Multi-stage triaxial test on brittle rock”; focus on brittle response and post-peak staging
Finds multi-stage can reproduce envelope but brittle instability and localization increase scatter and possible underestimation of peak strength if unloading chosen poorly.
Alsalman, (2015)
Comparison & proposed correction methods to map MST→SST results
Proposes corrections for systematic biases arising from damage accumulation; reports numeric adjustments/improvements.
Kotsanis et al., (2018)
Statistical processing of multistage tests; many stages per specimen
Demonstrates practical efficiency for scarce core material; discusses increased scatter for brittle lithologies.
McKean et al., (2019)
MFS applied to unconventional reservoir cores; demonstrated pre/post-peak characterization
MFS captured pre/post peak behavior for heterogeneous cores; recommended instrumentation improvements.
Table 2. Summary of automation, sensing, and data-driven approaches improving reliability and efficiency of MFS testing.
Technology/ Approach
Function in MFS Testing
Key Advantages
Representative Studies (2020–2025)
Automated closed-loop control
Real-time servo-hydraulic control of σ₁–σ₃; auto stage termination
Removes operator bias; improves reproducibility
Csuhanics & Debreczeni (2013); Jin et al. (2025)
Radial-strain-gradient (RSG) criterion
Objective stage termination
Rock-type independent; high repeatability
Jin et al. (2025)
Digital Image Correlation (DIC)
Surface strain mapping
Captures localization, non-contact
McKean et al. (2019);
Youn & Tonon (2010)
Acoustic Emission (AE)
Microcrack activity detection
Detects onset of damage
Choi et al. (2018);
Koosmen et al. (2023)
Fiber-optic sensing (FOS)
Distributed strain sensing
High spatial resolution
Gholizadeh et al, (2024)
Machine-learning analysis
Parameter inference from MFS data
Reduces human bias, handles nonlinearity
Trinh et al. (2025)
Digital twin coupling
Real-time model–test feedback
Predictive control, adaptive loading
Minaeian et al. (2020)

[1] MFS/CFS variant/method notes

[2] Main difference vs SST (qualitative)/reported bias

[3] Kovári and Tisa, (1975)

[4] Original Multiple Failure State and Strain-Controlled concepts; theoretical and early lab demonstration

[5] Introduces concept: derive multiple failure points from one specimen; emphasizes instrumentation and stopping rules.

[6] Kovári, et al. (1983)

[7] Continuous failure state / steady stress-path control; theoretical/procedural paper

[8] CFS maintains specimen at failure while changing stress path to trace envelope.

[9] Crawford and Wylie (1987)

[10] Modified MFS variants for reservoir cores — staged confining increases

[11] Used successfully for reservoir cores where sample availability limited; stresses that corrections and careful control required.

[12] Pagoulatos (2004)

[13] MFS variants; volumetric inflection / ΔV/V stopping criteria

[14] Generally close agreement for Berea sandstone with careful stopping rules; differences depend on stopping criterion (authors analyze sensitivity).

[15] Youn&Tonon, (2010)

[16] “Multi-stage triaxial test on brittle rock”; focus on brittle response and post-peak staging

[17] Finds multi-stage can reproduce envelope but brittle instability and localization increase scatter and possible underestimation of peak strength if unloading chosen poorly.

[18] Alsalman, (2015)

[19] Comparison & proposed correction methods to map MST→SST results

[20] Proposes corrections for systematic biases arising from damage accumulation; reports numeric adjustments/improvements.

[21] Kotsanis et al., (2018)

[22] Statistical processing of multistage tests; many stages per specimen

[23] Demonstrates practical efficiency for scarce core material; discusses increased scatter for brittle lithologies.

[24] McKean et al., (2019)

[25] MFS applied to unconventional reservoir cores; demonstrated pre/post-peak characterization

[26] MFS captured pre/post peak behavior for heterogeneous cores; recommended instrumentation improvements.

[27] Table 2. Summary of automation, sensing, and data-driven approaches improving reliability and efficiency of MFS testing.

[28] Technology/ Approach

[29] Function in MFS Testing

[30] Key Advantages

[31] Representative Studies (2020–2025)

[32] Automated closed-loop control

[33] Real-time servo-hydraulic control of σ₁–σ₃; auto stage termination

[34] Removes operator bias; improves reproducibility

[35] Csuhanics & Debreczeni (2013); Jin et al. (2025)

[36] Radial-strain-gradient (RSG) criterion

[37] Objective stage termination

[38] Rock-type independent; high repeatability

[39] Jin et al. (2025)

[40] Digital Image Correlation (DIC)

[41] Surface strain mapping

[42] Captures localization, non-contact

[43] McKean et al. (2019);

[44] Youn & Tonon (2010)

[45] Acoustic Emission (AE)

[46] Microcrack activity detection

[47] Detects onset of damage

[48] Choi et al. (2018);

[49] Koosmen et al. (2023)

[50] Fiber-optic sensing (FOS)

[51] Distributed strain sensing

[52] High spatial resolution

[53] Gholizadeh et al, (2024)

[54] Machine-learning analysis

[55] Parameter inference from MFS data

[56] Reduces human bias, handles nonlinearity

[57] Trinh et al. (2025)

[58] Digital twin coupling

[59] Real-time model–test feedback

[60] Predictive control, adaptive loading

[61] Minaeian et al. (2020)