# deteriorate

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The member is in like-new or as-built condition and has no deterioration.
The literature reveals that Markov models are extensively used to predict infrastructure deterioration [2, 15, 16] with bridges being a frequent candidate , followed by pavements  and sewer pipes [15, 17].
Applying the Markov process to predict the deterioration of navigation structures involves the following observations and assumptions.
where P is a function of X, representing the probability to change from state i to state j at time t + 1, for all deterioration states [i.sub.0], [i.sub.1], ..., [i.sub.t-1], [i.sub.t], [i.sub.t+1] and all t [greater than or equal to] 0.
When using the process to simulate deterioration, the following condition applies:
A further restriction allowing the condition to deteriorate by no more than one state in one rating cycle is commonly used in deterioration modeling.
From relations (4) and (8) results the expression of fatigue limit of sample loaded with average stress [[sigma].sub.m], having the residual stress ares and being subject to deterioration, [D.sub.T],
From relation (11) results that the fatigue limit of a sample without residual stresses ([[sigma].sub.res]=0), loaded with an average stress [[sigma].sub.m]>0, undergoing deterioration is lower than the fatigue limit of the virgin sample, without damage, stressed only alternant symmetrically ([[sigma].sub.m]=0).
Fatigue strength of the sample with deterioration after N<[N.sub.0] loading cycles results from relation
For N=[N.sub.0], with [D.sub.T]=0 the relation (13) gives the fatigue limit of the structure before deterioration, [[sigma].sub.-1,s] = [[epsilon].sub.d] x [[gamma].sub.s]/[K.sub.[sigma]] x [[sigma].sub.-1].
In this paper have been established relations for the calculus of fatigue limit (11), fatigue strength (12) and (13) and fatigue life (14) taking into account the influence of preloading deterioration and of characteristic parameters, i.e.

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