Background for Modeling

Krafft [4] and Krafft and Mulherin [5] later extended the TLI model to describe stress corrosion crack growth. Crack growth was viewed in terms of the instability of tensile ligaments where their lateral contraction was augmented by uniform chemical dissolution of the tensile ligaments. For sustained-load crack growth in an inert environment, on the other hand, the reduction in the cross-sectional area of the ligaments would be associated with the creep rate (Landes and Wei [2], Yin et aL 

Consider a ligament at the crack tip, with a current cross-sectional area A and true stress a, the load P carried by this ligament would be P = a A. At maximum load at the onset of tensile instability), the change in load would be zero i.e., 

For time-independent, power-hardening material (no creep)  

Similarly, for time-dependent, power-hardening material one that creeps), on the other hand, 

creep of the ligaments enhances the evolution of strain, and leads to earlier onset of tensile ligament instability hence, crack growth. 

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As additional background for modeling hydrate dissociation, it should be noted that there are three commonly cited classes of hydrate reservoirs in the permafrost, following the definition of Moridis and Collett (2004) ... 

Essential in multi-criteria decision analysis (MCDA) is the assiunption that when analysing such a multidimensional decision problem, the decision maker (DM) has a set of values, preferences, and that these values can somehow be modelled. One of the most used theories for this purpose is the multi-attribute value function theory (MAVT) (Belton Stewart, 2002). MAVT provides the background for modelling preferences by constructing a value function V(Ai) based on a comparison of outcomes in each criterion (scores) and a comparison of criteria (weights). In its simplest form, this value function is additive and can be written as in the following ... 

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