Mechanics of Lake Ice - Freezing of Lakes and the Evolution of their Ice Cover - page 146

Fig. 5.6 Creep of ice under a
constant load. The primary,
secondary and tertiary regimes
are shown

Creep

2

1

Stress=constant

Time

I II III

Table 5.2 Creep regimes in viscous deformation of ice under constant load

Regime Name Viscous law

I Primary creep Sub-linear

II Secondary creep Linear

III Tertiary creep Super-linear

Law y(x)=cx a is sub-linear for a < 1, linear for a = 1, and super-linear for a >1

Modelling these creep regimes is discussed in Schulson and Duval (2009) for glacier
ice. The primary creep is modelled as (Glen 1955).
e p ¼ e 0 þ b t

3 p þ e min t

ð 5 : 13 Þ

ʵ 0 is the instantaneous strain, and the transient strain e t ¼ b t

3 p is made of recov-

where

erable delayed elastic strain ʵ d and irreversible viscous strain (see Schulson and Duval

2009). Delayed elastic strain can be an order of magnitude larger than immediate elastic
strain, while transient creep can be two orders of magnitude larger than the elastic strain.
The secondary creep is well described by the Glen

' is (1955) law (see Paterson 1999)

e ¼ A r n

ð 5 : 14 Þ

where A and n are the flow law parameters. Data for the stresses in the range 0.2 2 MPa

-

support the value = 3, and for lower stresses the power is less than 3 (Schulson and

Duval 2009). The parameter

n

depends primarily on the temperature. In tertiary creep the
strain-rate increases from the minimum achieved in the secondary creep.
The Maxwell medium, where elastic and viscous models are connected in series, serves
as the basic model for ductile behaviour of ice. The viscous part is taken as a nonlinear
law, which is far preferable to the linear form. For a

A

fixed temperature the model can be
written in the form (see Glen 1955; Ramseier 1971; Ashton 1986)

n

e ¼ 1
E

r
E

r þ M D ð 5 : 15 Þ