Research Project B05

Hydromechanics of fractures and fracture networks: A combined numerical multi-scale and experimental investigation


Research Project B05 plans to cooperate closely on image-based characterisation and physical investigation of fractured rock with the group of Jens Birkholzer and Seiji Nakagawa at Lawrence Berkeley National Laboratory (LBNL, Berkeley).

A lively exchange of principal investigators and doctoral researchers between Berkeley and Stuttgart has existed for many years, especially in the field of fractured porous media systems. Recently LBNL has built an advanced laboratory for investigating the physics of hydraulic fracturing.


Data sets published by project B05 can be found on the DaRUS website

Publications in scientific journals

  1. Preprints

    1. Frey, S., Scheller, S., Karadimitriou, N., Lee, D., Reina, G., Steeb, H., & Ertl, T. (2021). Visual Analysis of Two-Phase Flow Displacement Processes in Porous Media.
    2. Schmidt, P., Jaust, A., Steeb, H., & Schulte, M. (2021). Simulation of flow in deformable fractures using a quasi-Newton based partitioned coupling approach. Zenodo.
    3. Lee, D., Karadimitriou, N., Ruf, M., & Steeb, H. (2021). Detecting micro fractures with X-ray computed tomography.
    4. Schmidt, P., Steeb, H., & Renner, J. (2021). Investigations into the opening of fractures during hydraulic testing using a hybrid-dimensional flow formulation.
  2. (Journal-) Articles

    1. Wagner, A., Eggenweiler, E., Weinhardt, F., Trivedi, Z., Krach, D., Lohrmann, C., Jain, K., Karadimitriou, N., Bringedal, C., Voland, P., Holm, C., Class, H., Steeb, H., & Rybak, I. (2021). Permeability Estimation of Regular Porous Structures: A Benchmark for Comparison of Methods. Transport in Porous Media.
    2. Yiotis, A., Karadimitriou, N. K., Zarikos, I., & Steeb, H. (2021). Pore-scale effects during the transition from capillary- to viscosity-dominated flow dynamics within microfluidic porous-like domains. Scientific Reports, 11(1), Article 1.
    3. Ruf, M., & Steeb, H. (2020). An open, modular, and flexible micro X-ray computed tomography system for research. Review of Scientific Instruments, 91(11), 113102--.
    4. Konangi, S., Palakurthi, N. K., Karadimitriou, N. K., Comer, K., & Ghia, U. (2020). Comparison of Pore-scale Capillary Pressure to Macroscale Capillary Pressure using Direct Numerical Simulations of Drainage under Dynamic and Quasi-static Conditions. Advances in Water Resources, 103792.
    5. Hasan, S., Niasar, V., Karadimitriou, N. K., Godinho, J. R. A., Vo, N. T., An, S., Rabbani, A., & Steeb, H. (2020). Direct characterization of solute transport in unsaturated porous media using fast X-ray synchrotron microtomography. Proceedings of the National Academy of Sciences.
    6. Karadimitriou, N. K., Mahani, H., Steeb, H., & Niasar, V. (2019). Nonmonotonic Effects of Salinity on Wettability Alteration and Two-Phase Flow Dynamics in PDMS Micromodels. Water Resources Research.
    7. Steeb, H., & Renner, J. (2019). Mechanics of Poro-Elastic Media: A Review with Emphasis on Foundational State Variables. Transport in Porous Media.
    8. Hasan, S. N., Joekar-Niasar, V., Karadimitriou, N., & Sahimi, M. (2019). Saturation-Dependence of Non-Fickian Transport in Porous Media. Water Resources Research.
    9. Yin, X., Zarikos, I., Karadimitriou, N. K., Raoof, A., & Hassanizadeh, S. M. (2019). Direct simulations of two-phase flow experiments of different geometry complexities using Volume-of-Fluid (VOF) method. Chemical Engineering Science, 195, 820--827.
    10. Zhang, H., Frey, S., Steeb, H., Uribe, D., Ertl, T., & Wang, W. (2018). Visualization of Bubble Formation in Porous Media. IEEE Transactions on Visualization and Computer Graphics, 1–1.


About this project

The aim of this project is to characterize fractures and fracture networks based on a combination of physical experiments, image-based methods, and numerical simulations. The focus of all the investigations lies on the fundamental understanding of hydromechanical coupling effects of (deformable) fluid-saturated fractures embedded in a deformable porous material. Project B05 aims at providing the scientific community with detailed information and further insight into i) the development and evolution of preferential flow paths in fracture networks, ii) the role of asperities in the non-linear effective hydromechanical coupling between fractures, iii) the possibility of back-analyze  the fracture properties in the case of non-linear hydromechanical coupling, iv) the role of leak-off in crystalline rocks, and v) whether the same concepts can be applied on fractures saturated with more than one fluid phase.

Micro-XRCT data set of Carrara marble with artificially created crack network: fast cooling down from 600°C.


For the performance of image-based characterization and in-situ XRCT investigations, the existing experimental facilities at the Porous Media Lab (PML) have been substantially enhanced. We have successfully developed and applied a new X-ray transparent cell, also used in synchrotron studies. This cell allows the characterization of multi-phase/multi-component flow processes in porous materials under controlled confining stress conditions, by applying a confining pressure.  Additionally, an X-ray transparent triaxial cell for stress states up to 20 MPa has been designed and successfully implemented into our XRCT in situ set-up. In this new triaxial cell the triaxial stress states, and the confining/pore pressure can be individually controlled, offering the ability to employ bigger rock samples (diameter of ¼ inch). Surfaces of cores can be prepared (e.g. grinded and accurately polished) and even miniaturized strain gauges can be implemented due to the bigger size. The open XRCT device was also upgraded with a 10 kN uniaxial testing device for mechanical in situ experiments. In order to tackle the ring artefacts due to unresponsive detector pixels, we implemented a method to slightly shift the detector’s position and combine the acquired information to account for the lost information.

Dongwon Lee

For the investigation of complex fracture networks, we quenched (gradual increase and sudden decrease of temperature) a Bianco Carrara marble. The corresponding samples were characterized with standard techniques for their effective properties before and after treatment. Additionally, the topology of the fracture network was investigated with μ-XRCT. For the effective characterization of the fracture network, the segmentation the μ-XRCT data had to be performed. In order to compare the segmentation efficiency, we adopted three conventional segmentation methods and two machine learning segmentation methods. For the conventional segmentation methods, the application of a data noise reduction technique before segmentation was essential for the success of the process. That was not necessary in the machine learning schemes, which eventually saves computation time. However, given that the training of the machine learning model required excessive memory, the images were diced into small tiles in order to avoid a memory limitation issue. The U-net machine learning scheme was proven to be the most effective approach to segment the μ-XRCT data.

The in-house developed Digital Rock Physics (DRP) workflow was also employed to complement the experimental approach with XRCT-based Stokes simulations for large REVs (up to10003 voxels. An explicit high performance Stokes solver has been developed and it is currently being tested for voxel-based geometries XRCT scans.

Numerical investigation of harmonic pressure stimulated fracture.

We also focused on the hydro-mechanical coupling in a fracture. A numerical investigation was performed which was able to reproduce a non-linear relation between flux and pressure caused by a volume change, under a harmonic pressure-/flow stimulation of a single fracture under confining stress. Under the same conditions, a benchmark experiment was conducted on an aluminum sample with rough fracture surfaces. This artificial fracture was stimulated with a harmonic flux of a fluid via an induced bore hole and the corresponding induced pressure was measured. As a way to show the non-linearity in the relation between flux and pressure under a harmonic stimulation, we present the measured corresponding pressure in the frequency domain. In both the numerical and experimental investigation, overtones were observed which imply the non-linear response of the system.

Harmonic numerical and laboratory measurement on the aluminum sample.

However, an artificially induced fracture may hold different properties such as storativity, diffusivity and contact stiffness, from natural fractures. For further realistic investigation of the harmonic stimulation on a single fracture, we introduced a single fracture in a sandstone sample by hydraulic pressure. Performing the harmonic experiment on this realistic sample is ongoing work.

Microfluidic investigations have also been performed in order to understand the hydromechanical interaction of “soft” fractures embedded in Poly-di-methyl-siloxane (PDMS) We investigated the intrinsic pressure diffusion time of single fractures and fracture networks with respect to the fluid’s viscosity and the elastic properties of PDMS.

Future work

Project B05, in the process of addressing the open questions stated in the beginning, the following steps will be made.

Fractured rock, microfluidic, and numerical investigations will take place in the attempt to address the objectives of the project. This includes μ-XRCT investigations of natural samples both in-the-house, and in a synchrotron environment for fast, time-resolved 3D characterization. Additionally, 2D, time- and space-resolved microfluidic investigations will take place, both with “soft” and “hard” micromodels. Complementary to the experimental investigations, numerical investigations will be performed, also in a supplementary manner for the flow domains that cannot be materialized with microfluidics due to technical limitations.

International collaborations

With our external partners from the Lawrence Berkeley National Laboratory, Dr. Jens Birkholzer and Dr. Seiji Nakagawa, we will perform transient/harmonic rock physics experiments under lithostatic stress states. Further, we are aiming at the analysis, clustering and visualization of high-resolution XRCT data obtained from static and, especially, dynamic synchrotron investigations, in collaboration with our external partners at the University of Manchester (Dr. Vahid Joekar-Niasar).

For further information please contact

This picture showsHolger Steeb
Prof. Dr.-Ing.

Holger Steeb

Principal Investigator, Research Projects B05 and C05

This picture showsWolfgang Nowak
Prof. Dr.-Ing.

Wolfgang Nowak

Principal Investigator, Research Projects B04 and B05

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