---

I²

л²

In⁴EI
у loo-e

where

/ is the moment of inertia of one single pipe;

N_cr is the axial compressive force in the single pipe;

f > ■ ■ is the initial deflection;

° 200

/_s is a safety factor, y_s = 1,1.

For pipe sections entirely locked by friction:

Л/ = -{A _s■ (e ■ a ■ AT - v ■ a _p)+ p ■ A _p}

where

/t_s is the cross-sectional area of the steel pipe;

a is the coefficient of thermal expansion of the steel;

AT is the temperature increase from equilibrium temperature (where N = 0) to maximum temperature;

v is Poisson’s ration (v- 0,3 for steel);

<j_p is the hoop stress from internal pressure;

p is the internal pressure (maximum operating pressure);

A_p is the area the pressure is acting on.

Q can be calculated from Q = G^ + G + 2 S_F

where

Gn/ is the effective weight of soil stratum over the pipe per metre of pipe length;

G is the effective selfweight of the preinsulated pipe per metre of pipe length;

S_F is the shear force, which can result from the soil pressure at rest shown in the dashed vertical cut in

Figure B.11.

Figure B.11 — Stabilising vertical soil pressure

For ground-water table below the pipes:

G = Z D_c~— f^| у ^and S_F=--/ Z K_o tan^

2 I 2 2

V ' /

If the groundwater table is above the bottom of the pipe the effective density of the soil and the buoyancy of the pipe must be taken into account.

Normal forces reduced due to resulting buckling are not taken into account in these calculations.

B.5.3 Horizontal stability

Securing sufficient side support is of particular importance when using curved pipes, small angular deviations or in the case of parallel excavation.

Parallel excavations at the side of the district heating pipes demand that the "local" stability of the slope is in order considering an outwards horizontal force towards the slope at the size Pfor single pipes and 2 Pfor pipe pairs.

Moreover, the overall stability of the slope must be in order, as no stabilising effect from the pipes may be included in the calculations.

In case of parallel excavations above and/or beside buried district heating pipes, during the operating phase adequate provisions should be taken to ensure:

1. that the pipes are horizontal and vertical stable, according to B.5, in order to prevent flexural buckling,

2. that the increased movements of the pipe system at the expansion zones caused by reduced pipe to soil friction are within allowable limits with regard to stresses and displacements.

In situations with length-wise excavations, directly above the pipes, the friction force is calculated, corresponding to the reduced depth of burial.

Reduction of friction force as a consequence of excavating at one side of the district heating pipes may be assumed to be an approximate maximum of 35%. The reduction can be completely ignored if the distance between excavation side and district heating pipe exceeds 2 times the excavation depth.

When a district heating pipeline is laid in soft soils, and sand is used for backfill, the bedding constants for the sand should not be used in the calculations. The actual values will be lower and are to be determined taking into account the lower stiffness of the surrounding soil.

Similarly there is no reason to make special effort to reach a high degree of compaction of the sand backfill. Because of the deformation of the softer soils around the sand backfill, the effective soil to pipe pressure (and thus the friction value) will show relaxation.

Special attention should be paid to transition zones between pipes in a buried trench and pipes on fixed vertical support such as:

1. bored or jacked crossings under roads, etc. especially when an additional casing pipe is used,

2. wall penetrations at house connections.

When sand backfill is applied in peat or soft clay soil settlement prediction should be based on a local soil mechanics study. The results should be clearly presented as ultimate values.

A realistic system of axle loads, such as will actually occur in the operating life of the pipeline, shall be the basis.

Application rule:

Load models used should comply with ENV 1991-3:2003. For national highways and regional roads, "Load Model 3" including exceptional transports) can be assumed. For lower category roads, "Fatigue Load Model 2, Lorry 4" can be taken. The latter load system covers the "set of frequent lorries", as may occur on European roads, with the exception of special transports.

In the open field also "Fatigue Load Model 2, Lorry 4" can be taken, with all axle loads divided by a factor 2,0.

Alternative methods for calculation of traffic loads may be derived from CEN/TR 1295-2.

Due attention shall be paid to traffic loads, caused by (temporary) heavy construction traffic, during the installation phase of a pipeline, or due to activities of third parties above existing pipelines.

The distribution of axle loads in the subsoil can be calculated according to the method of Boussinesq or Braunstorfinger. [8]. Reference is made to CEN/TR 1295-2.

The traffic load per length unit:

Q_v = P_v x D_o

where

Q_v is the traffic load, in kN/m, at pipe top level;

D_o is the outside diameter, including coating, in m;

P_v is the traffic load at pipe top level, caused by the axle load system, in kN/m².

The load-relieving influence of road constructions may be discounted in the calculation of the traffic load, in the following cases:

1. road constructions consisting of a multiple-layer system, i.e. one or more foundation layers have been laid on the subsoil and finished with a top layer;

2. road constructions, whereby the subsoil is or has been paved with asphalt or concrete.

The calculation method converts the effect of the foundation layer and top layer into a (fictional) equivalent depth of soil cover on the pipe. Subsequently the traffic load at pipe top level is calculated, using this equivalent depth of cover. In case of a three-layer system (subsoil, foundation layer and top layer) for example, the foundation layer is first converted to an equivalent soil cover, and the same procedure is followed for the top layer. The equivalent depth of cover (Н^) is then obtained by: H₃+ /-/_1eq+ H_2eg= H^.

The formula that shall be used for calculating the equivalent depth of cover:

H_n,_eq=0.9xH_nx^_n/E_g

where

H_n is the thickness of the layer to be converted;

E_n is the elasticity modulus of the layer to be converted;

Eg is the elasticity modulus of the subsoil.

Top of pavement

Hl

Top Layer

Foundation

H₂

Subsoil

Figure B.12 — Calculation of equivalent soil cover

Table B.4 includes typical values which can be used in calculations. Other values than those indicated may be used if it is satisfactorily demonstrated by new or existing research that these different values are correct.

Application rule:

The formula for the equivalent depth of cover can also be written as: He, = H + aH<, + BH₂, whereby a is dependent on covering layer and В is dependent on the foundation layer. In case of a certain thickness of the top layer (Hi), thickness of the foundation layer (H₂) and a depth of cover H, the equivalent depth of cover (Heq) can be calculated with this formula. Values for a and В have been included in Table B.4

.

Table B.4 — Typical values for different top layers and foundation layers

B.8.2 Stresses and ovalization from top load

The interaction between pipe and soil in circumferential direction is represented by a system of soil springs (pipeline considered as a ring). This gives the load diagram as shown in Figure B.13

Key 1 top of pipe

2. top load (soil + traffic)

3. top load angle a (= 180°)

4. bottom of pipe

5. vertical soil supprt pressure

6. vertical soil support angle 0

7. side of pipe

8. neutral horizontal soil pressure

9. horizontal support pressure from pipe ovalisation

10. horizontal soil support angle у (=120°)

11. horizontal support diagram for sand

12. horizontal support diagram for clay/peat

Figure B.13 — Load diagram for directly transmitted vertical load

B.8.2.2 Directly transmitted vertical load

For straight pipe sections, not subject to internal pressure, the circumferential stress is given by:

_a M_tot _ KxQ_totxr_g

⁴ W_w W_w

where

M_tot is the tangential moment in the pipe wall due to Q_tot;

К is the moment coefficient, as a function of load angle (a), support angle (₽) and position on the ring

circumference, see Table B.5;

Qtot is the total vertical load;

Qtot IS Q_s + Qv Qeg Qvut ^— Qop, Q_op is the upward force by buoyancy.

For tangentially flexible pipes under internal pressure, “re-rounding” (from internal pressure) may be taken into account:

„ -f M^L-f „^KxQ™^XI9 ^{4 T}rr _w- hr*

^vvw

where where

f_n = 1

2p_dxr_g³ xk_y
£x/_w

frr is the “re-rounding”-factor;

p_d is the design pressure, in N/mm²;

k_y is the deflection factor (see Table B.5).

Application rule:

Theoretically, when calculating bending moments due to Q_eg and Q_vui„ moment coefficients other than for Q„ should be used; the effect on the end result is, however, negligible. In many cases, the effect of Q_eg and Q_vui on M_tot can be neglected.

Table B.5 — Moment coefficients and deflection factors for directly transmitted vertical load

B.8.2.3 Horizontal support pressure from trench backfill compaction

In soft soils (Soft clay and peat), only neutral horizontal earth pressure is taken into account.

Application rule:

Applying a sand backfill in soft soil will only temporarily increase the horizontal pressure.

In sandy soils and in stiff clay with sand backfill, it is possible to increase the neutral horizontal earth pressure with the horizontal support pressure (caused by ovalisation of the pipe), thus reducing circumferential bending stresses.

In this case, the trench backfill is mechanically compacted.

Reference is made to CEN/TR 1295-2 for overview and details of calculation methods.

Application rule:

The reliability of the calculation method is dependant, to a great degree, on the actual execution of the trench backfill compaction works as well as its continuity overtime.

B.8.3 Deflection

B.8.3.1 General

Deflection of the ring diameter in a unpressurized condition, without horizontal soil support, can be calculated with the formula:

ky xQ_tot xr³

L

H

where

Qtot Q_v Q_s k_y 6_U

/_w

is the total vertical load;

is the traffic load, in N/mm:

is the effective vertical earth load, in N/mm;

is the deflection factor (see Tables D.1 and D.2);

is the vertical deflection.

In sand, horizontal passive earth pressure (see Figure D.2) can be taken into account and the deflection can be calculated with the following formula (Spangler):

_s _ PxQ_tot xr³(k_y -0.0834)

^Y E/_w+0.061 xk_h xr_g

where

D is the ‘deflection lag’ (creep) factor related to lateral consolidation. D is ranging from 1.5 for soft clays, peat and uncompacted sand to D = 1.0 for well-compacted sand (95 % or more of the Maximum Proctor Density);

k_h is the modulus of horizontal subgrade reaction in N/mm³;

A_n is the coefficient of neutral horizontal earth pressure (A_n =1 — sin <p).

Application rule:

If D = 1.5 is applied with lower values of k_h, the second formula may give a higher deflection than the first formula, which does not take into account horizontal earth resistance. In this case, the lowest value, arrived at by one of the two formulas given above, can be used.

The calculated deflection can be used to calculate the lateral support pressure, assuming a lateral support angle of 120 and a sinusoidal lateral soil pressure distribution.

Subsequently the bending moments from the lateral support pressure can be calculated, using coefficients from Table B.5 and subsequently combined with the bending moments from vertical loads.Annex C
(informative)

Global- and cross sectional analysis

C.1 General

Annex C has status as application rule.

Annex C describes a method for verifying the required resistance of a pipe system to force- and displacement- controlled actions.

The method and assessment specified in this standard presupposes that:

1. ductile materials are used for the system;

2. a bi-linear, elasto-plastic material model is used for the soil;

3. a pseudo-elastic material model is used for the steel assuming purely linear elastic material behaviour, also for stresses exceeding the yield strength.

Alternatively a plastic material model can be used. The calculation in this case is based on an elastic-plastic stress­strain relation of the material. In such case the assessment of stresses and strains are different from the specifications in this standard.

When calculating internal forces, stresses and deformations the rigidity of individual components and the stress concentrations occurring for different action combinations shall be taken into account.

C.2 Symbols

l_b,l_r Extent of increased wall thickness for branch and run pipe

M_z Bending moment

M_x Torsional moment

N_x Axial force, including pressure contribution

NFP Natural fixpoint

p Internal pressure

r_b,r_m Stress reduction factors for branch and run pipe

r,r-i,r_x Radii of curvature

R Bend radius

S Stress range

t_n Nominal wall thickness of service pipe

t Nominal wall thickness of pipe less possible allowance for tolerance and corrosion

t_bit_r Nominal wall thickness of branch and run pipe less possible allowance for tolerance and corrosion

Vy, V_z Shear force

W Section modulus of pipe cross section

a Thermal expansion coefficient

a, 0 Angle

v Poisson's ratio

G_a, g_x Axial stress

cr_m Membrane stress

cr_res Resulting stress

Reference stress for membrane stresses

O/res Reference stresses for resulting stresses

CTp Hoop stress

G_t Tangential stress