Diethard König

Experimental investigation of shear band patterns in granular material

Abstract This paper presents three series of sandbox experiments of extensional deformation in granular material. The dependence of the developing shear band system on different boundary conditions and material properties is investigated: (1) granulometric properties of the material, (2) initial geometry of the specimen, and (3) dynamic material parameters. Particular attention is paid to the controlling of the basal boundary conditions. X-ray technique and particle image velocimetry (PIV) are used to study the changes in the granular structure and in the formation of shear band patterns. The results show that boundary conditions are an elaborate factor to explain differences in the shear band pattern. It is shown that neither the average grain size diameter d 50 nor the rate of loading influences the shear band spacing. The spacing of the bands seems to be linearly dependent on the initial height of the specimen.

Sensitivity analysis and parameter identification of a time dependent constitutive model for rock salt

The tendency to shift from fossil and nuclear energy sources to renewable energy carriers has increased during the past couple of decades. Subsequently, development of effective energy storage systems has become more attractive. Nowadays, caverns excavated in rock salt formations are recognized as the appropriate places for underground storage of energy in the form of compressed air or hydrogen. Accurate design of these underground cavities requires suitable numerical simulations employing appropriate constitutive models to describe the material behavior of rock salt under various geological conditions. It is obvious that to have a realistic numerical simulation, it is essential to have a comprehensive knowledge concerning the unknown material parameters and their influence on the calculation results. In this paper, a time dependent model is selected to describe the mechanical response of the rock salt around the cavern. This model is implemented in a finite element code and its application in numerical modeling of salt caverns is illustrated. In addition, global sensitivity analysis is used to investigate the influence of material parameters on the mechanical behavior of the salt cavern. Finally, inverse analysis of the synthetic data is performed to identify the material parameters of the selected model. The applied global sensitivity and inverse analysis algorithms employ metamodeling technique in order to reduce the time which is needed for these computationally expensive calculations.

Concept for an integral approach to explore the behavior of rock salt caverns under thermo-mechanical cyclic loading in energy storage systems

The fluctuating nature of renewable energy sources can be managed by storing the surplus of electrical energy in an appropriate reservoir. The excess electricity available during off-peak periods of consumption may be used to compress air or electrolyze hydrogen. Afterward, the pressurized gas is stored in the rock salt cavities and discharged to compensate the shortage of energy when required. During this process, the rock salt surrounding the cavern undergoes thermo-mechanical cyclic loading. In order to achieve a reliable geotechnical design, the stress–strain response of rock salt under such loading condition has to be identified and predicted. In order to investigate the rock salt behavior under such loading, a comprehensive study using three concepts of geotechnical engineering, i.e., experimental investigation, constitutive modeling and numerical analysis, is conducted. A triaxial experimental setup is developed to supplement the knowledge of the cyclic thermo-mechanical behavior of rock salt. The imposed boundary conditions in the experimental setup are assumed to be similar to the stress state obtained from a full-scale numerical simulation. The computational model relies primarily on the governing constitutive model for predicting the behavior of rock salt cavity. Hence, a sophisticated elasto-viscoplastic creep constitutive model is developed to take into account the dilatancy and damage progress, as well as the temperature effects. The contributed input parameters in the constitutive model can be calibrated using the experimental measurements. In the following, the initial numerical simulation is modified based on the calibrated constitutive model. However, because of the significant levels of uncertainties involved in the design procedure of such structures, a reliable design can be achieved by employing probabilistic approaches. Therefore, the numerical calculation is extended by statistical tools such as sensitivity analysis, optimum experimental design, back analysis, probabilistic analysis and robust reliability-based design to get final design parameters of paramount need for practice.

Probabilistic Analysis of a Rock Salt Cavern with Application to Energy Storage Systems

This study focuses on the failure probability of storing renewable energy in the form of hydrogen or compressed air in rock salt caverns. The validation of the short- and long-term integrity and stability of rock salt cavern is a prerequisite in their design process. The present paper provides a reliability-based analysis of a typical renewable energy storage cavern in rock salt. An elasto-viscoplastic creep constitutive model is implemented into a numerical model of rock salt cavern to assess its behavior under different operation conditions. Sensitivity measures of different variables involved in the mechanical response of cavern are computed by elementary effect global sensitivity method. Subset simulation methodology is conducted to measure the failure probability of the system with a low computational cost. This methodology is further validated by a comparison with a Monte Carlo-based probabilistic analysis. The propagation of parameter uncertainties and the failure probability against different failure criteria are evaluated by utilizing a Monte Carlo-based analysis. In this stage, the original finite element model is substituted by a surrogate model to further reduce the computational effort. Finally, a reliability analysis approach is employed to obtain the minimum admissible internal pressure in a cavern.

Numerical simulation of deep and shallow energy storage systems in rock salt

The design and safe operation of caverns in rock salt need an accurate stability analysis. This paper provides the results of a geomechanical survey on the stability of a typical hydrogen underground storage. To accompolish this, first the behaviour of the cavern is analysed by a numerical model, taking into account the nonlinear creep behaviour of the rock salt. Then, the safety of the cavern is evaluated by comparing stress states for different regions around the cavern with a compression/dilatancy (C/D) boundary. Different depth of cavern’s roof location and various internal loads are considered. Results show minimum values for internal cavern pressure to guarantee the stability of the cavern for different depth of cavern location.