Abstract
An important parameter involved in the viscoelastic deformation of structural materials is the coefficient of “solid” viscosity. Determination of this parameter is necessary, if it is to be used in structural design.
This paper deals with pertinent analytical considerations concerning solid viscosity and describes the procedures followed in the determination of parameters for structural and true viscosity of a Queenston limestone. The following three techniques were used:
-
(1)
Relaxation technique
-
(2)
Uniaxial compressive loading
-
(3)
Cantilever-beam loading
The results obtained are in close mutual agreement except for (2) above, where experimental conditions were different from those in (1) and (3).
A quasi-periodic behavior of strain is indicated. It has been shown that the solid viscous parameter is a transient property and may depend on such factors as applied load, time, grain size, grain-packing in a material, and the direction of testing.
It has been concluded that coefficients of true and structural solid viscosity of materials can be determined for a given set of conditions.
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Abbreviations
- A :
-
direction parallel to the bedding plane of dolomite
- η:
-
coefficient of viscosity
- ηR :
-
coefficient of relaxation viscosity
- ηRA :
-
coefficient of relaxation viscosity in direction A
- ηRB :
-
coefficient of relaxation viscosity in direction B
- ηRC :
-
coefficient of structural viscosity in direction C
- ηs :
-
coefficient of structural viscosity
- ηT :
-
coefficient of true viscosity
- ηsh :
-
coefficient of viscosity in shear
- B :
-
direction normal to the bedding plane of dolomite
- C :
-
direction normal to both directions A and B in dolomite
- d :
-
effective thickness of cementing material between grains, also, the differential symbol
- dP :
-
stress differential
- dx :
-
distance slipped by grain along the graincement interface in dolomite
- D g :
-
average grain diameter
- E :
-
Young's modulus of elasticity
- e :
-
2.7183 (base of Napierian logarithms)
- ε:
-
unit
- ε1:
-
major principal strain
- ε2:
-
minor principal strain
- (∈1 - ∈2):
-
shear strain
- \(\overline {( \in _1 - \in _2 )} \) :
-
shear-strain gradient
- γ:
-
shear strain
- γ0 :
-
initial shear strain
- \(\dot \gamma \) :
-
shear-strain gradient
- G :
-
modulus of rigidity
- G u :
-
unrelaxed modulus of rigidity
- I :
-
moment of inertia
- l :
-
length of a sample, of a mine stope
- l o :
-
initial length of a sample, of a mine stope
- P :
-
applied force, compressive load
- σ:
-
unit stress
- σ1 :
-
major principal stress
- σ2 :
-
minor principal stress
- (σ1 - σ2):
-
shearing stress
- t :
-
time
- T :
-
time of relaxation
- r :
-
shear stress
- v :
-
rate of relative displacement of grains on two sides ofd
- W :
-
width, also diameter
- Y :
-
deflection at the end of a cantilever beam
- \(\dot Y\) :
-
velocity of sagging of the free end of a cantilever beam, made of a viscous material
- ϕ:
-
coefficient of viscosity in tension.
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Rana, M.H. Experimental determination of viscosity of rocks. Experimental Mechanics 9, 538–549 (1969). https://doi.org/10.1007/BF02316656
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DOI: https://doi.org/10.1007/BF02316656