Analyzing an underground piping system presents circumstances quite different from those encountered when analyzing plant piping. The major problem is the accurate modeling, using point restraints, of the continuous effects of soil-pipe interaction. The pipe-soil interaction, which resists piping movements and forces, are divided into two categories — frictional forces, which must be overcome by pipe sliding against the soil, and pressure forces, which are caused by the pipe pushing against the soil.
Axial friction force is calculated as the product of the soil-pipe friction coefficient and the total normal force acting around the pipe. An example of a pipe buried in a trench is shown in Figure 3-117. In this case, the normal force acting on the pipe surface can be simplified as a top force W (for cases where the soil cover ranges from one to three times the pipe diameter, this is approximately equal to the weight of the soil above the pipe), and a bottom force, equal to the weight of the pipe plus the soil above it. Therefore the frictional force offering axial restraint on the pipe is estimated as:
The soil density and friction coefficient can be obtained from soil tests performed along the pipe route. Where data is not available, the following values are typical:
Silt — 0.3 Sand — 0.4 Gravel — 0.5 Clay = 0.6 to 2.4
Pressure forces are caused when the pipe tries to move laterally, pushing against the soil. Three different lateral soil forces normally encountered in piping analysis are shown in Figure 3-118. Each lateral restraint response can be idealized, as shown in Figure 3-118d, into two response stages: elastic, where the resisting force is proportional to the pipe displacement, and plastic, where resistance remains constant regardless of displacement. This type of restraint can be modeled using a bi-linear restraint, specifying an elastic stiffness, an ultimate load (for the elastic to plastic transition), and a plastic stiffness (which should be near zero). The soil will not only restrain the pipe against movements, but through couples, against rotations as well.
The stiffness of the soil restraint (in lb/in per inch of pipe) can be calculated as the product of the soil modulus of elasticity times the outer diameter of the pipe. In the event that the soil modulus is not known, the stiffness can be determined from other soil parameters. For example, for sidewards motion, a passive pressure is created at the front surface of the pipe. According to L. C. Peng's paper "Stress Analysis Methods for Underground Pipelines" (published in the May 1978 edition of Pipe Line Industry), the ultimate load and idealized elastic response can be estimated from various soil parameters, as:
In order to sufficiently simulate the continuous effect of soil restraint, it is often necessary to break underground piping into a finer mesh than would be necessary for plant piping.
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