The two-dimensional Mandel-type problem geometry is well-known to bio-geomechanicians for testing rocks, cartilages, and bones with solutions in Cartesian coordinates for rectangular specimens or polar coordinates for cylindrical and disk samples. To date, all existing solutions are only applicable to single-porosity and single-permeability models, which could fall short when the porous material exhibits multiporosity and/or multipermeability characteristics, such as secondary porosity or fracture. This paper extends the plane strain and axisymmetric Mandel-type solutions from single-to dual-porosity and dual-permeability poromechanics. The solutions are presented in explicit analytical forms and account for arbitrary time-dependent external loading conditions, e.g., cyclic and ramping. The derived analytical solutions and results exhibit general behaviors characterized by two time scales. Stresses, pore pressures, and displacements are plotted for various time scale ratios to illustrate the interplaying effects of permeability and stiffness contrast of both porous regions, in addition to the interporosity exchange, on the overall responses of the system. Also, examples with realistic loading conditions for laboratory testing or field simulation such as cyclic and ramping are provided to demonstrate the engineering applications of the presented dual-poroelastic formulation and solutions.
Skip Nav Destination
e-mail: nxvinh@ou.edu
e-mail: yabousle@ou.edu
Article navigation
January 2010
Research Papers
Poromechanics Solutions to Plane Strain and Axisymmetric Mandel-Type Problems in Dual-Porosity and Dual-Permeability Medium
Vinh X. Nguyen,
Vinh X. Nguyen
Mewbourne School of Petroleum and Geological Engineering, PoroMechanics Institute,
e-mail: nxvinh@ou.edu
University of Oklahoma
, Sarkeys Energy Center, Suite P119, 100 East Boyd Street, Norman, OK 73019
Search for other works by this author on:
Younane N. Abousleiman
Younane N. Abousleiman
Mewbourne School of Petroleum and Geological Engineering, ConocoPhillips School of Geology and Geophysics, School of Civil Engineering and Environmental Science, PoroMechanics Institute,
e-mail: yabousle@ou.edu
University of Oklahoma
, Sarkeys Energy Center, Suite P119, 100 East Boyd Street, Norman, Oklahoma 73019
Search for other works by this author on:
Vinh X. Nguyen
Mewbourne School of Petroleum and Geological Engineering, PoroMechanics Institute,
University of Oklahoma
, Sarkeys Energy Center, Suite P119, 100 East Boyd Street, Norman, OK 73019e-mail: nxvinh@ou.edu
Younane N. Abousleiman
Mewbourne School of Petroleum and Geological Engineering, ConocoPhillips School of Geology and Geophysics, School of Civil Engineering and Environmental Science, PoroMechanics Institute,
University of Oklahoma
, Sarkeys Energy Center, Suite P119, 100 East Boyd Street, Norman, Oklahoma 73019e-mail: yabousle@ou.edu
J. Appl. Mech. Jan 2010, 77(1): 011002 (18 pages)
Published Online: September 23, 2009
Article history
Received:
September 5, 2008
Revised:
May 24, 2009
Published:
September 23, 2009
Citation
Nguyen, V. X., and Abousleiman, Y. N. (September 23, 2009). "Poromechanics Solutions to Plane Strain and Axisymmetric Mandel-Type Problems in Dual-Porosity and Dual-Permeability Medium." ASME. J. Appl. Mech. January 2010; 77(1): 011002. https://doi.org/10.1115/1.3172146
Download citation file:
Get Email Alerts
Sound Mitigation by Metamaterials With Low-Transmission Flat Band
J. Appl. Mech (January 2025)
Deformation-Dependent Effective Vascular Permeability of a Biological Tissue Containing Parallel Microvessels
J. Appl. Mech (January 2025)
Mechanics of a Tunable Bistable Metamaterial With Shape Memory Polymer
J. Appl. Mech (January 2025)
Related Articles
Theory and Analytical Solutions to Coupled Processes of Transport and Deformation in Dual-Porosity Dual-Permeability Poro-Chemo-Electro-Elastic Media
J. Appl. Mech (November,2018)
Radiation Loading of a Cylindrical Source in a Fluid-Filled Cylindrical Cavity Embedded Within a Fluid-Saturated Poroelastic Medium
J. Appl. Mech (September,2002)
Effect of Wick Characteristics on the Thermal Performance of the Miniature Loop Heat Pipe
J. Heat Transfer (August,2009)
Determination of Optimum Design Parameters for Gyroid Scaffolds to Mimic a Real Bone-Like Condition In Vitro: A Fluid Structure Interaction Study
ASME J of Medical Diagnostics (August,2023)
Related Proceedings Papers
Related Chapters
Introduction and Definitions
Handbook on Stiffness & Damping in Mechanical Design
The Development, Implementation, and Use of ASTM C1701 Field Infiltration of In Place Pervious Concrete
Pervious Concrete
Completing the Picture
Air Engines: The History, Science, and Reality of the Perfect Engine