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A.6 Dished ends

A.6.1 General

Dished ends shall be ellipsoidal ends, made on a truly ellipsoidal former (Fig A.4) that fulfil the following requirements:

• Uniform wall thickness

• 1.7<K<2.2 (K is shape factor of dished end = dj/2.hj

• z—1

• R < d₀

• R/d, = 044K + 0.02

d> t

do

Figure A.4 — Ellipsoidal Dished Head

where

h, is inside height of ellipsoidal end;

R is inside radius of curvature of central part of ellipsoidal end.

A.6.2 Minimum required wall thickness for internal pressure

The minimum required wall thickness is:

',=——

2-cTy.z-0.5-/^

where

t_s = minimum thickness of end to limit membranes stress in center.

Application rule:

Dished ends of other shapes may be applied, if calculated according to a relevant international or national standard.

Unflanged flat ends, as described in section 7.2.3.3 of EN 13480-3, are normally not allowed.

A.6.3 Straight cylindrical shells

If the length of the straight cylindrical part of the dished end exceeds: it shall also meet the requirements of Clause A.3.

Annex В
(informative)

Geotechnics and pipe-soil interaction

This annex has status as an application rule.

For hot buried pipelines subject to large deformations and axial forces, the calculated bending moments and forces are strongly dependent on the correct modelling of the pipe-soil interaction and the reliability of soil parameters used.

This Annex provides guidance on:

1. the relevant parameters for pipe-soil interaction analysis (B.3),

2. methods for obtaining characteristic values for soil parameters (B.4),

3. requirements for specific areas of attention (B.5-B.7).

The methods of analysis and soil parameters selected for design must be appropriate for the intended pipeline system and the proposed route and facilities and must be compatible with all potential actions and failure mechanisms. Methods of calculating the magnitude of deformation can be based upon numerical modelling, empirical relationships or combinations thereof.

у Effective density of soil

(p Angle of internal friction of soil

ц Coefficient of interface friction between soil and PE casing

Reference is made to C.6.1.

For a static calculation of the system (global analysis) the forces due to pipe-soil interaction may be represented by a beam-element model comprising three components as shown in Figure B.1. The pipeline may be represented by a simple structural beam with the reactions from the soil f, p and q modelled as discrete soil springs k_x, k_y and k_z.

Figure B.1 — Modelling pipe-soil interaction

It is normally assumed that there are no shear stresses between two adjacent springs, along the pipe axis laying springs or bedding elements.

As an alternative for discrete springs, theories for beams on elastic foundation or finite element methods can be used.

The amount of restraint is usually a non-linear function of the relative motion between soil and pipe as illustrated in Figure B.2 where f-u, p-v and q-w refer to axial, horizontal and vertical reactions and displacements respectively.

If displacements greater than u_u, v_u and w_u occur the soil reactions may reach constant ultimate values of f_u, p_u and q_u respectively.

Figure B.2 — Load-deformation relationship

Normally the most important restraints are:

1. the axial restraint f-u, given by the pipe to soil friction, see B.3.2,

2. the horizontal restraint p-v, given by the horizontal modulus of soil reaction, see B.3.3.

B.3.2 Pipe to soil friction (axial)

The relevant ultimate values of the friction f_u between PE casing and surrounding soil must be determined in due consideration of the installation conditions such as:

a) type of backfill material and method and degree of soil compaction, b) maximum and minimum groundwater levels,

3. presence of very stiff street covers preventing lateral soil displacements, d) influence of possible future parallel excavations nearby the pipes,

e) “tunnel effect” due to possible increase in friction because of pipe diameter increase when heating up and friction reduction because of pipe diameter decrease when cooling down.

For sandy soils the relative displacement u_u between pipe and surrounding soil required to reach the maximum friction resistance f_u is approx. u_u = 1 - 3 mm.

The maximum friction resistance can be calculated as:

f_u ~ A where

a_n is the effective normal stress along the periphery of the PE casing.

For sandy soils the normal stress at a casing can be calculated on basis of a state of soil pressure at rest, giving the friction per unit length of pipe:

r- b + K₀„ (D_r V'

' /

where:

K_o is the coefficient of soil pressure at rest, K_o = 1 - sin^>;

For sandy soils Kq may normally be valued at 0,5;

G is the effective selfweight of pipe with water; a_v is the effective soil stress at pipe centre level. For granular soils:

H_w+j'_sw(Z-H_w) forH_w<Z

CT_V= Ys'Z for H_W>Z

where

H_w is the depth of ground water table below grade, see Figure B.3;

y_s is the effective density of soil above ground water table;

y_SM is the effective density of soil below ground water table = y_sw - y_w;

is the density of saturated soil below ground water table;

Xv is the density of water.

Key

1 Grade 2 Groundwater table

Figure B.3 — Calculation of effective soil stress

Friction coefficient

The friction coefficient //should be determined with due consideration of the soil type, size and shape of the grains, compaction of soil backfill and deformation velocity.

For sandy soils // may be calculated as:

H = tan 3

where

8 is the angle of interface friction between soil and pipe.

For sandy soils and PE casing Jmay be taken as approximately equal to 2/3 (p, with a maximum value of 8 approximately 20-22.

For sandy soils, which are not settlement areas, typical design values for // used for fatigue analysis and design of expansion provisions can be taken from Table В 1.

Table B.1 — Friction coefficients for sandy soils

NOTE 1 For large diameter pipes in well-graded sand there is a risk for the so-called tunnel-effect when cooling down. The tunnel-effect can give expansions equivalent to fl = 0 - 0,2. The low values should be used e g. when designing expansion facilities.

NOTE 2 For low cycle fatigue analysis an average value should be used. In most cases // = 0,4 is considered appropriate.

NOTE 3 Specific local soil condition should be taken into account.

B.3.3 Coefficient of horizontal soil reaction (lateral)

The coefficient of horizontal soil reaction or horizontal bedding constant is defined as the ratio between horizontal soil pressure and horizontal movement of the pipe system.

^к"=^£<Г^Е^> v Length

where

p is the horizontal soil reaction;

v is the relative horizontal movement between pipe and soil.

The value к = k_h. D_c (Force/Length²) is defined as the line bedding constant.

For buried pipes without expansion cushions a fair relationship between horizontal pipe movement and corresponding soil restraint is given by:

v

P v_u

^Pu 0,15 + 0,85 —

v_u

where:

p_u is the maximum soil pressure mobilised by deformation v_u;

p is the soil pressure, p < p _u and v < v_u corresponding to the deformation v.

The horizontal bedding constant, which is the secant modulus of the action-displacement diagram, can be deducted from the expressions above:

P,

v 0,15 v_u + 0,85 v

The p - v diagrams show elastic soil behaviour at smaller displacements represented by the bedding value and plastic soil behaviour at large displacements represented by the ultimate horizontal bearing capacity.

For modelling a bi-linear action-displacement diagram may be used where the bedding constant is chosen as 70 % of p_u divided by the corresponding displacement, see Figure B.4.

For small displacements the k_h value referring to 50 % p_u can be used.

The ultimate horizontal soil resistance p_u can be assessed using the equivalent action capacity formula for side support (in cohesion-less soils):

where

K_q is the soil pressure coefficient, see Figure B.5.

The ultimate horizontal displacement v_u is not defined precisely. The results of a number of tests with small diameter pipes are summarised in Table B.2.

Table B.2 — Ultimate horizontal displacement v_u

NOTE Values obtained by interpolation.

Alternatively values derived from calculations or tests on anchor plates can be used.

B.3.3.2 Influence of large depths or stiff street cover

The failure mechanism at the plastic stage which strongly influences the ultimate value depends on the depth of burial. At shallow or intermediate depths the failure zone will be extended to the surface with a passive front wedge and an active wedge at the backside of the pipe. At burial depths greater than approximately 6-10 D_c. The plastic zone will develop as a limited flow zone in front of the pipe. The dimensions of this flow zone are dependent on the degree of soil compaction, see Figure B.6.

Key

1. Failure surface

2. Zone of flow of the soil

Figure B.6 — Failure mechanism of soil at horizontal pipe displacement

For pipes laid at shallow depths under a stiff street surface, e.g. concrete, the failure mechanism with the passive front wedge is prevented and a failure mechanism with a limited flow zone may occur. This leads to a much higher horizontal soil reaction than normally encountered at these depths.

Actual stiffness of the cover as well as the pipe diameter influence the result. For very stiff street cover (e.g. concrete slaps or pavement for heavy traffic) FEM analysis indicate that a relation between pipe displacement and soil restraint (re. Figure B.4) for dense sand and a stiff road cover 0,4 m thick can be established as follows:

For H > 1 m v_u and p_u are multiplied by 3,8.

For H < 1 m the values for H - 1 m can be used.

Stiff street cover is e.g. concrete slaps and asphalted roads for heavy traffic. Higher horizontal soil reactions may also result from frozen soil around the pipes, to be taken into account with e.g. soils containing clay in northern climate.

For light street cover a factor < 3,8 can be chosen.

v

Key

1. With stiff street cover

2. Without stiff street cover

Figure B.7 — Soil reaction for stiff street cover

B.3.4 Combined stiffness of PUR foam, expansion cushions and soil

In expansion zones the combined stiffness of steel pipe, PUR foam, PE casing, expansion cushions and surrounding soil should be calculated to a combined value for the line bedding constant.

The combined line bedding constant can be derived from the bedding constants of the different components. However, in the following only PUR, expansion cushions and soil are considered, deformations from steel pipe and PE casing are left out due to their small size.

The total horizontal deformation is equal to the sum of the deformation of PUR foam (v₇), expansion cushion (v₂) and surrounding soil (v₃). This means that normally 3 serial springs have to be combined.

For practical calculations the stiffness of the PE casing can be deleted, as it has little influence on the result. The stiffness of the steel pipe may be taken into account only for large diameter pipes, e.g. d₀> 610 mm.

Calculation of the bedding constant for the expansion cushions should take account for the non linear load­deformation curve of the cushions.

^fPUR t_Cu

Key

1. Cushion

2. PE

3. PUR

4. Steel

5. Soil

Figure B.8 — Symbols for bedding constants

1. PUR foam:

L- _ P PUR 1г — lr ri ^KhJ - . > ^K1 - ^Kh,1 °o

‘PUR

2. Expansion cushion:

The plate bedding constant for expansion cushions should be taken from the load-displacement curve based on the actual deformation, see 6.5.2.

^h,2 ~ I к2 = k_{h 2}■ D_c

CU

3. Surrounding soil:

к = ^{0,7 P}-^u- , k₃=k_h3■ D_cu see B.3.3 and Figure B.4

^л'³ v(70%) ^{3 h}'^{3 cu} where

E_cu is the elasticity modulus of the cushions, see 6.5;

t_cu is the equivalent thickness of the cushions;

D_cu is the equivalent outside diameter of the cushions.

The combined load-displacement curve can be calculated from:

Key

1. Soil

2. Cushion

3. Resulting curve

Geotechnical parameters for axial and transverse (lateral) stability and deformational analysis should be selected in accordance with good engineering practice taking due account of the stochastic variation of soil properties.

When the limits of variation of the soil properties are well known (i.e. granular sandy soils), use may be made of standard values and methods, as presented in B.3.

In other cases, especially when large variations in soil properties are to be expected, or when the pipeline system is installed in soft soils (containing clay and peat) and settlement areas, a local soil mechanics study may be required, according to B.4.2.

Excavation and backfill procedures should be performed and safeguarded such that the values for soil parameters, as used in the design calculations, are sufficiently guaranteed.

In case a local soil mechanics study is required to define reliable values for pipe-soil interaction allowance should be made for various uncertainty sources:

1. Field examinations are carried out at a limited number of points along the pipeline axis and the soil properties in between these points may deviate;

2. Difference in soil sampling procedures;

3. Laboratory work deriving the parameters for pipe-soil interaction from the results of borings, cone penetration tests and soil samples, making use of theoretical models.

When mean values (having a probability of 50% to be exceeded) are presented, these should be multiplied or divided by contingency factors (load variation factors) to arrive at the characteristic upper or lower values required for pipeline analysis (having a probability of 5% to be exceeded).

The results of the soil mechanics study should therefore clearly be presented as ultimate values or as mean values.

The soil mechanics report must further clearly state whether and which contingency factors have been taken into account.

Contingency factors for soil parameters, referred to mean value, are presented in Table B.3 [ref. EN 1594:2000].

Table B.3 — Contingency factors for soil parameters referred to mean value

In a state with large axial compressive forces in the pipes there may be a risk of buckling due to column effect (global instability). Therefore, the depth of burial must be sufficient to allow the upper backfill to provide stability.

E> deleted text О

Vertical stability should be examined in the case of:

1. little soil cover,

2. high groundwater level,

3. excavations over the pipes.

The remaining soil action shall be sufficient to withstand a vertical upward reaction equal to 2Q for pipe pairs and equal to Q for single pipes.

For an "infinitely" long, partly straight pipe section with equally distributed vertical load Q per unit length of pipe (from backfill and selfweight of pipe) buckling can be avoided if:

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