Time-dependent resistance | Library builder

For a hydraulic structure placed in a natural environment over a period of time, its operational characteristics could change over time owing to deterioration, aging, fatigue, and lack of maintenance. Consequently, the structural capacity (or resistance) would vary with respect to time. Examples of time-dependent characteristics of resistance in hydrosystems are change in flow-carrying capacity of storm sewers owing to sediment deposition and settlement, decrease in flow-carrying capacity in water distribution pipe networks owing to aging, seasonal variation in waste assimilative capacity of natural streams, etc.

Modeling time-dependent features of the resistance of a hydrosystem requires descriptions of the time-varying nature of statistical properties of the resistance. This would require monitoring resistance of the system over time, which, in general, is not practical. Alternatively, since the resistance of a hydrosystem may depend on several stochastic basic parameters, the time — dependent features of resistance of hydraulic structures or hydrosystems can be deduced, through appropriate engineering analysis, from the time-varying behavior of the stochastic parameters affecting the resistance of the systems. For example, the flow-carrying capacity of a storm sewer depends on pipe slope, roughness coefficient, and pipe size. Therefore, the time-dependent behavior of storm sewer capacity may be derived from the time-varying features of pipe slope, roughness coefficient, and pipe size by using appropriate hydraulic models.

Although simplistic in idea, information about the time-dependent nature of stochastic basic parameters in the resistance function of a hydrosystem is generally lacking. Only in a few cases and systems is partial information available. Table 4.6 shows the value of Hazen-Williams coefficient of cast iron pipe types

TABLE 4.6 Typical Hazen-Williams Pipe Roughness Coefficients for Cast Iron Pipes

Age (years) new	Pipe diameter all sizes	Roughness coefficient Chw 130
5	>380 mm (15 in)	120
	>100 mm ( 4 in)	118
10	>600 mm (24 in)	113
	>300 mm (12 in)	111
	> 100 mm (4 in)	107
20	>600 mm (24 in)	100
	>300 mm (12 in)	96
	> 100 mm (4 in)	89
30	>760 mm (30 in)	90
	>400 mm (16 in)	87
	> 100 mm (4 in)	75
40	>760 mm (30 in)	83
	>400 mm (16 in)	80
	> 100 mm (4 in)	64

SOURCE: After Wood (1991).

as affected by pipe age. Owing to a lack of sufficient information to accurately define the time-dependent features of resistance or its stochastic basic parameters, it has been the general practice to treat them as time-invariant quantities by which statistical properties of resistance and its stochastic parameters do not change with time.

The preceding discussions consider the relationship between resistance and time only, namely, the aging effect. In some situations, resistance also could be affected by the number of occurrences of loadings and/or the associated intensity. If the resistance is affected only by the load occurrences, the effect is called cyclic damage, whereas if both load occurrence and its intensity affect the resistance, it is called cumulative damage (Kapur and Lamberson, 1977).

Related Posts: