Benjamin Cerfontaine

Cyclic and Fatigue Behaviour of Rock Materials: Review, Interpretation and Research Perspectives

The purpose of this paper is to provide a comprehensive state of the art of fatigue and cyclic loading of natural rock materials. Papers published in the literature are classified and listed in order to ease bibliographical review, to gather data (sometimes contradictory) on classical experimental results and to analyse the main interpretation concepts. Their advantages and limitations are discussed, and perspectives for further work are highlighted. The first section summarises and defines the different experimental set-ups (type of loading, type of experiment) already applied to cyclic/fatigue investigation of rock materials. The papers are then listed based on these different definitions. Typical results are highlighted in next section. Fatigue/cyclic loading mainly results in accumulation of plastic deformation and/or damage cycle after cycle. A sample cyclically loaded at constant amplitude finally leads to failure even if the peak load is lower than its monotonic strength. This subcritical crack is due to a diffuse microfracturing and decohesion of the rock structure. The third section reviews and comments the concepts used to interpret the results. The fatigue limit and S–N curves are the most common concepts used to describe fatigue experiments. Results published from all papers are gathered into a single figure to highlight the tendency. Predicting the monotonic peak strength of a sample is found to be critical in order to compute accurate S–N curves. Finally, open questions are listed to provide a state of the art of grey areas in the understanding of fatigue mechanisms and challenges for the future.

Validation of a New Elastoplastic Constitutive Model Dedicated to the Cyclic Behaviour of Brittle Rock Materials

AbstractOld mines or caverns may be used as reservoirs for fuel/gas storage or in the context of large-scale energy storage. In the first case, oil or gas is stored on annual basis. In the second case pressure due to water or compressed air varies on a daily basis or even faster. In both cases a cyclic loading on the cavern’s/mine’s walls must be considered for the design. The complexity of rockwork geometries or coupling with water flow requires finite element modelling and then a suitable constitutive law for the rock behaviour modelling. This paper presents and validates the formulation of a new constitutive law able to represent the inherently cyclic behaviour of rocks at low confinement. The main features of the behaviour evidenced by experiments in the literature depict a progressive degradation and strain of the material with the number of cycles. A constitutive law based on a boundary surface concept is developed. It represents the brittle failure of the material as well as its progressive degradation. Kinematic hardening of the yield surface allows the modelling of cycles. Isotropic softening on the cohesion variable leads to the progressive degradation of the rock strength. A limit surface is introduced and has a lower opening than the bounding surface. This surface describes the peak strength of the material and allows the modelling of a brittle behaviour. In addition a fatigue limit is introduced such that no cohesion degradation occurs if the stress state lies inside this surface. The model is validated against three different rock materials and types of experiments. Parameters of the constitutive laws are calibrated against uniaxial tests on Lorano marble, triaxial test on a sandstone and damage-controlled test on Lac du Bonnet granite. The model is shown to reproduce correctly experimental results, especially the evolution of strain with number of cycles.

A Case Study of a Long-Duration Thermal Response Test in Borehole Heat Exchangers

Shallow closed-loop geothermal systems are worldwide applied providing economical and environmental benefits. This paper presents an in-situ study of four Borehole Heat Exchangers of 100 m long, installed in an heterogeneous bedrock in the campus of the University of Liege (Liege, Belgium). A Thermal Response Test (TRT) of a heating phase of 7 months was conducted in one of the boreholes. During this test, temperature was measured at the pipe inlet and outlet, as well as along the four boreholes by the fiber optics. To further investigate the measured data, the test was simulated by 3D numerical modeling. The comparison of the measured data with the numerical results allowed to detect the critical parameters for the behavior of the BHE and for the temperature evolution in the surrounding rock mass. In this case study, the behavior of the BHE could be predicted based on the results of a typical-duration TRT (of a few days), considering the ground an homogenous and isotropic material. However, the thermal plume in the surrounding ground seems to be influenced by several factors, such as the bedrock heterogeneity, the distance to the heating source, air temperature variations and thermal effects at the borehole bottom end.