Buried Pipeline Model

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Interaction between the pipeline and surrounding soil is analyzed using methods developed by A.B. Aynbinder for Start-Prof (at that time called "ST-01"). Methods are based on experimental and theoretical research conducted at VNIIST (Moscow) and other organizations, and is a version of methods described in [1] and [6].

Start-Prof soil model consider:

Model Description

Start-Prof uses a beam pipeline model, where interaction of pipeline and soil is modeled with longitudinal and transverse spring supports (bilinear springs), places at certain intervals (fig. 1).

 

1 - Vertical soil spring, 2 - Axial soil spring, 3 - Lateral soil spring

Fig. 1. Pipeline and soil interaction model

 

Springs are placed automatically. Three zones are marked around the nodes where supports are more closely placed (fig. 2):

If several operating modes are specified in operation mode editor, then first sustained operating mode is used for La and Lb calculation and these values are used for all operating modes.

The number of supports in the area of strong longitudinal and transverse displacements is increased automatically; i.e., nodes:

 

Fig. 2. Placement of supports modeling soil interaction

Lateral Bearing Zone #1 (Unrestrained)

Lateral bearing zone #1 have a big bending deformations and transverse displacement (fig. 3). To increase model accuracy, four soil springs are automatically placed here.

lateral bearing length can be calculated using:

,

where

- pipe bending stiffness,

- soil stiffness factor.

Fig. 3. Bend zone #1

Axial Sliding Zone #2 (Unrestrained)

Axial sliding zone #2 have a big longitudinal deformations and displacements (fig. 4). To increase model accuracy, four supports are placed with exponential increasing spacing from zone #1 to zone #3.

 

 

Virtual anchor length for an elastic-plastic soil model  [6] can be calculated using equation (more information on this):

 

Fig. 4. Sliding zone #2

Restrained Zone #3

There is no bending and no axial displacements in the restrained zone. Therefore, soil springs are placed at a large spacing, equal to 100D

Soil Resistance Model

Soil support stiffness is calculated as the overall stiffness of several springs (fig. 5).

Stiffness K1 is a non-linear function dependent on cushion deformation. Can also be calculated based on empirical dependence from experiment results [3]. Presence or absence of cushioning pads is set in  buried element properties.

Stiffness K2 is a non-linear function dependent on PUR layer deformation and is calculated based on empirical dependence from experiment results [3]. To calculate PUR stiffness, insulation casing diameter must be input in buried element properties.

Stiffness of springs modeling soil depends on their direction (fig. 5). There are three types:

Fig. 5. Accounting for the stiffness of the PUR-insulation layer and cushioning pads

The general model of algorithms for the correlation of reactions in springs and displacement is shown on fig. 4. The algorithm values are calculated based on input  buried element properties, as well as base and back-fill soil properties set in  the soil database.

Springs restricting lateral displacement in the horizontal plane  K3 have a reaction and displacement correlation shown on fig. 6.a. Vertical and longitudinal springs are shown on fig. 6.b and fig. 6.c, respectively.

After starting an analysis, Start-Prof automatically runs a series of consecutive analyses and at each step clarifies the stiffness value of all springs K1, K2, K3, K4 and K5. When a certain accuracy is achieved, the analysis is stopped.

 

Fig. 6. Non-linear correlation of soil resistance and displacement in various directions relative to the pipe axis

Analysis of Vertical and Inclined Pipe Elements with Variable Depth

Depth, water height and subsidence can change along the pipe length, so these properties are input at the beginning ZH, HBH, ΔH and the end ZK, HBK, ΔK of each element (fig. 6). Depth, water height and subsidence are basically input for nodes, not elements. So these values must be the same for a node, even if it belongs to two adjoining elements. For example, if depth changes for a node of one element, depth will automatically change for this node of the other adjoining element.

 

Fig. 6. Depth and water height based on element length

 

When the properties of each set of three springs K3, K4 and K5 are analyzed, various depth Zi and water height HBi values determined by linear iteration of start and node nodes ZH and ZK are used (fig. 7). Water buoyancy is also calculated based on water height HBi at each point. Subsidence value for each spring Δi is calculated in a similar way, using linear iteration ΔH, ΔK.

Properties of springs  K3, K4 and K5 also depend on the angle of slant relative to the horizontal plane (from 0 to 90 degrees). For vertical elements K4=K3.

Fig. 7. Spring depth for elements with fluctuating depth

Accounting for Water Buoyancy

Buoyancy acting on the pipe and soil resistance to vertical and longitudinal pipe displacement depends on water height HB (properties of suspended soil are considered).

For horizontal, vertical and slanted elements, only the pipe section which is under water is considered in buoyancy analysis (fig. 8).

Fig. 8. Calculation of the volume of displaced liquid for buoyancy analysis

Soil Subsidence

When the soil subsides, for example, due to melting of base soil or construction near the pipeline area, there is no resistance from the base and the pipeline subsides along with the soil  (fig. 9).

Fig. 9. Pipeline with soil subsidence

The subsidence process can be described using the correlation model shown on fig. 6.b and shifting it to the left by the value of base subsidence  Δ (fig. 10). This model is equivalent to the displacement of springs modeling vertical downward soil displacement (along the Z axis) by the value of Δ (fig. 9).

The value of subsidence due to melting or compression of base soil layers can be determined, for example, using SNIP  [5].

To model frost heave (upward displacement), the subsidence value must be negative.

Fig. 10. Correlation of soil resistance to vertical displacement taking into account subsidence

Soil Resistance to Longitudinal Pipe Displacement

Soil resistance to vertical pipe displacement in the area of elastic-plastic deformation can be modeled as linear correlation, proposed by A.B. Aynbinder [1].

where

- maximum allowable soil resistance to displacement, N/sm2,

- generalized tangent soil resistance factor N/sm3,

- working displacement value corresponding to maximum soil resistance to displacement, cm.

Dependence is obtained by substituting the true diagram of soil resistance to longitudinal displacement (fig. 11.a) with an idealized bilinear diagram (fig. 11.b).

Fig. 11. Dependence of soil resistance to longitudinal displacement

Tangent soil resistance factor is expressed as:

and has the dimensions of the soil bed factor during displacement. In the soil database this value is referred to as the resistance to longitudinal displacement factor. The factor shows the slant of the first section of the bilinear diagram, shown on fig. 11.b.

To input a rigid-plastic soil model without taking into account elastic resistance, the tangent resistance factor must have a very high value (fig. 12). In practice, a large number, for example 100000 tf/m3 can be used. If the database has the value =0, then Start-Prof uses a value equal to 100000 tf/m3.

Fig. 12. Elastic-plastic and rigid-plastic soil models

Values of values adapted from A.B. Aynbinder's experimental data for various soil types are provided in table 1.

Table 1. Generalized tangent soil resistance factor values, MPa/sm

Soil Type

Allowable Soil Consistency Values IL

Soil Properties with Porosity Factor  ε

<0.5

0.5-0.6

0.6-0.7

0.7-0.8

>0.8

Coarse and medium gravel sand - 0.03 0.03 0.027 0.025 -
Fine and silty sand - 0.025 0.021 0.021 0.019 -
Sandy loam 0 < IL ≤ 0.25 0.035 0.033 0.03 0.03 0.03
0.25 < IL ≤ 0.75 0.035 0.032 0.03 0.025 0.025
Loam 0 < IL ≤ 0.3 0.038 0.035 0.035 0.032 0.03
0.3 < IL ≤ 0.75 0.035 0.033 0.03 0.025 0.02
Clay 0 < IL ≤ 0.3 0.04 0.038 0.035 0.033 0.03
0.3 < IL ≤ 0.75 0.045 0.04 0.035 0.03 0.03

If experimental data for the value of are not available, the following approximation formula can be used:

where

- soil bed coefficient during displacement corresponding to the thickness of the soil layer above the pipe, h1, of 1 m,

η - reduction factor according to table 2 when the thickness of the soil layer above the pipe, h2, exceeds 1 m. Depends on the h1/h2 relationship.

Table 2. Reduction factor η

h1/h2 1.0 0.8 0.6 0.5
η 1.0 0.9 0.8 0.75

Approximately values of the soil bed factor for various soil types adapted from [4] are listed in table 3.

Table 3. Soil bed factor values during displacement given backfill height above the pipeline of h1=1.0 m

Soil , N/sm3
Sandy loam 5.0
Loan 4.0
Dry peat 0.5
Moist peat 1.0

References

1. Aynbinder A., Kamerstein A. Analysis of the transmission pipelines for strength and stability. Moscow "Nedra" .1982

2. Skomorovsky Ya.Z., Ainbinder AB, longitudinal movement of buried pipelines taking into account physical nonlinearity soil shear resistance. Pipeline strength questions, Moscow 1975

3. Arbeitsblatt FW 401: Verlegung und static von KMR für Fernwärmenetze Arbeitsgemeinschaft Fernwärme- AGFW-e, V.- bei der Vereinigung Deutscher Elektrizitätswerke, 1992

4. Borodavkin P. Buried transmission pipelines (design and building), Мoscow "Nedra, 1982

5. SNiP 2.02.04–88. Foundations located on permafrost. Gosstroy USSR. Мoscow, 1991

6. Aynbinder A., Kamerstein A. Analysis of the transmission pipelines and flowlines for strength and stability. Мoscow "Nedra", 1991