Thermal and Mechanical Behaviors of a Saturated/Frozen Rock Sample under Sub-Zero Temperature

2006 Fiscal Year Final Research Report Summary

• Project/Area Number: 16560056
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Materials/Mechanics of materials
• Research Institution: Iwate University
• Principal Investigator: KURASHIGE Michio Iwate University, Faculty of Engineering, Professor, 工学部, 教授 (20005416)
• Co-Investigator(Kenkyū-buntansha): FURUZUMI Mitumasa Iwate University, Faculty of Engineering, Professor, 工学部, 教授 (20003874) ; HIROSE Kouichi Iwate University, Faculty of Engineering, Professor, 工学部, 教授 (80156710) ; IWAI Kazuwo Iwate University, Faculty of Engineering, Research Associate, 工学部, 助教 (70113850)
• Project Period (FY): 2004 – 2006
• Keywords: Simulation / Thermal Strain / Freezing Strain / Moving Boundary Problem / Boundary Fixing Method / Latent Heat / Micromechanics / Mixed Region

Research Abstract

A laboratory test found that (1)water-saturated cubic rock samples shrink as the ambient temperature goes down from room temperature, (2)they abruptly, steeply and tremendously expand at a subzero temperature, leaving large positive strains, (3)they gradually contract with further temperature lowering down to-170℃, (4)they keep contracting even for the temperature kept constant, with positive strains still left, (5)they start to expand as the temperature rises, and (6)they steeply shrink a while after the positive temperature is reached, leaving large residual strains. Such a strain history associated with the temperature cycle was considered related to thermal strains and volume expansion due to freezing of pore water contained in rock samples.
To understand such an observed strain history of the rock samples against the temperature cycle from the room, down to subzero, and back to room temperature, the present paper simulates thermal and mechanical behaviors of a spherical rock sample subjected to a similar temperature cycle as in experiments.
Lowering of the ambient temperature cools the sample and freezes pore water from its surface, while a temperature rising process brings about melting of the frozen ice in pores from the surface; resulting in movement of freezing or melting fronts. Therefore, the present problem is one of the moving boundary value problems. Temperature fields are analyzed by resorting to the boundary fixing method and the Crank-Nicolson finite difference scheme.
Thermal stresses and strains are estimated for the spherical sample from the obtained temperature fields. In addition, the time-dependent distribution of freezing stresses and strains are calculated by use of a formula, derived based on the micromechanics, for volumetric strain induced due to pore water freezing. Elastic moduli required in these calculations are estimated using the Mori-Tanaka formula, in which rocks are assumed to be a composite of rock substance and water or ice.
From the strain analysis described above, total strains on the sample surface are estimated and drawn against the ambient temperature during the temperature cycle for a few values of Biot number. Comparison of the total strain-ambient temperature diagrams obtained shows a good qualitative agreement with that by experiments.