Durodrain System Design

DURODRAIN uPVC SOLID WALL SEWER AND DRAIN PIPE SYSTEMS (SANS 791)

SYSTEM DESIGN

Plastic pipe systems, in particular PVC-U, are economical and a practical material for sewer applications.
Flexible pipes are recognised as having benefits over rigid pipes with regard to load shedding.
The flexibility, although resulting in higher deformation, has the following advantages over rigid pipe:

  • Yield under vertical soil load reduces the total soil load as more friction is transferred to the sides of the trench.
  • Pipe carries relatively less load than the sidefill as it yields i.e. it sheds load to the sidefill.
  • The pipe deflects out laterally thereby activating soil support and creating an arching action.
  • Yielding of plastics results in stress redistribution across a section, thereby utilizing the entire section in load resistance.

SOIL/PIPE INTERACTION

The mode of failure of a pipe can be due to circumferential or longitudinal overloading. This section addresses concerns regarding external loads which cause circumferential stress. . Flexible PVC pipes deflect under the influence of vertical external loads and the reactive support of the surrounding soil. Failures can occur due to high bending, arching stresses in the wall (more common for rigid pipes) or buckling. In the case of flexible pipes, the stiffness of the surrounding material can be more important in limiting deflection than the stiffness of the pipe itself, so controlled backfill is particularly important.
The load transmitted to a pipe from the external surrounding depends on a number of factors:

Rigidity of pipe

The more rigid a pipe is relative to the trench sidefill, the more load it will take. The sidefill tends to settle, thus causing a large part of the backfill to rest on the pipe. This occurs with flexible pipe to some extent, as a pipe is supported laterally by the fill and will not yield as much as a free standing pipe.

Type of trench

The load transmitted to the pipe varies with the width and the depth of the trench since friction on the sides of the trench effects the resultant load. Various trench conditions are illustrated below. (Refer SANS 0102 (1) for more detail).

Narrow trench: Maximum friction  least load on the pipe
Narrow trench: Maximum friction -
least load on the pipe
Wide shallow trench: Less friction  more susceptible to superimposed loads such as vehicles
Wide shallow trench: Less friction -
more susceptible to superimposed
loads such as vehicles
Wide trench  deep embankment: Least friction  greater load on the pipe
Wide trench -
deep embankment: Least friction -
greater load on the pipe

The vertical load due to soil is generally the most severe from the point of view of deflection and circumferential bending stress. Under embankments of cohesionless and frictionless soil, the vertical pressure at the level of the top of the pipe could be evaluated using column theory to be:

W = GHD
where W is the download on pipe (kN/m)
H is the depth (m)
G is the unit weight of soil (kN/m³)
D is the external pipe diameter (m)

The load must generally be corrected because the soil is cohesive and the sidefill reacts with the fill over the pipe. In addition, flexible pipes yield and shed load to the sidefill, thus the net load in kN per unit length of pipe is often less than what the column theory indicates.

Most pipes are laid in trenches and friction in the side of the trench supports some of the fill. The load in kN/m, i.e. per unit length of width B is thus:

F = C1GHB
C1 is evaluated in Figure 1 as a function of H/B and k tan Ø
where k is the ratio of lateral to vertical soil stress =
(1- sin Ø)
__________
(1+ sin Ø)
and Ø is the soil angle of friction

Load co-efficients for trench conditions
Load co-efficients for trench conditions Diagram

Flexible pipes yield more than the sidefill and therefore the load is shed to the soil. The net soil load in kN/m of pipe is thus:

Ws = CƒF
and

=

8EI/ND3 + Es/2K

________________________
8EI/ND3 + (1/2K+B/D-1)Es
where

E is the pipe elastic modulus (Pa)
Es is the soil modulus (Pa)

I is the moment of inertia of the pipe wall (mm4/mm) = †3

_____

12

† is the wall thickness (m)
D is the outside diameter (m)
N is the deflection coefficient which is a function of the bending angle
K is the sidefill lag factor
B is the trench width (m)

Typical values for the soil modulus, Es (MPa) are shown in the table below.

Soil modulus as a function of density

Soil type Compaction
Loose 85% 90% 95%
Gravel Stone 7 20 30 50
Sand - 12% fines 3 7 15 20
Silt LL< 50% 1 3 5 10
Clay LL > 50% 0.1 1 3 7

DEFLECTION

Vertical deflection is limited by lateral soil resistance as the pipe tends to deflect outwards laterally. The load is thereby taken in arch action rather than circumferential bending, so wall stresses are considerably less than for rigid pipe, The deflection in metres allowing for load shedding is:

Δ d




= Ws
Ws

Ps + Ss

8EI/ND3 + Es/2K
= Ws

8 E†3/D3 + 0.4Es
where Ws is the load on pipe (kN/m)
Ps is the pipe stiffness (Pa)
Ss is the soil stiffness (Pa)

The E values for DURODRAIN PVC-U Sewer pipes, which decrease with age, to be used for soil load and deflection calculations are:

Instantaneous, E = 2500 x 106 N/m²
Minimum 50 year, E = 1500 x 106 N/m²

For live loading, one should perform a separate calculation using the short term E value and add up the two deflections caused by soil and live loads.

% Deflection =
Δd

x 100
D

Deflection of PVC-U Sewer Pipe under Load

Deflection of PVC-U Sewer Pipe under Load Diagram

EXAMPLE: DEFLECTION

Calculate the deflection and maximum wall stress of a 315 mm diameter DURODRAIN heavy duty sewer pipe (wall thickness 9.20 mm) under 3m of average soil in a 900mm wide trench. Take the soil modulus as 3MPa, soil mass 2000kg/m³ or 20kN/m³ and long term modulus 1500MPa. Take bottom support over 90°, N = 0.095, Nm = 0.13 and sidefill lag factor 1.5, soil friction angle = 12°.

Trench load F at 3m = C1GHB

when H/B = 3/0.9 = 3.3
and k tanØ = (1 - sin12)/(1 + sin 12) x tan12° = 0.13
then C1 = 0.65 (figure 1)
F = 0.65x20x3x0.9
= 35.1kN/m
Load on pipe WS = CƒF
where = 8EI/ND3 + ES/2K
8EI/ND3 + (1/2K + (B/D)- 1)ES
= [8 (1.5 x 109) (0.00923/12)/(0.095)(0.3153)]+ [(3 x 106)/(2 x 1.5)]
[8(1.5x 109)(0.00923/12)/(0.095)(0.3153)] +[((1/2 x 1.5) + (0.9/0.315)) -l] (3 x 106)
= 262 245.60 + 1 000 000.00
262 245 .60 + 6 571 428.57
= 0.1847
therefore WS = 0.1847x35.1
6.483 kN/m of pipe
Soil pressure w = 6.483/0.315
= 20.58 kN/m²
Δ d = WS
8E†3/D3 + 0.4 ES
= 6.483 x 103
[8 x ((1500 x 106)(0.00923))/ 0.3153 + 0.4 (3 x1O6)]
=

6 483

__________________

1 498 959.99

= 0.0043m
deflection % =
Δd

D
X 100
=
0.0043

0.315
X 100
= 1.37%

LIVE LOADS FROM SOIL SURFACE

Pressure on the pipe in kN/m² due to a live load of P (kN) on the surface of the soil is:

W1 = 3PH3
2 ? (H2 + X 2 ) 5 / 2
where P is the live load (kN)
X is the lateral distance to live load P (m)
H is the depth to the crown of the pipe (m)

The live load per metre of pipe, W1 = w1 D, should strictly be corrected for load shedding, but it activates a higher pipe modulus, E, than the soil load does, as it is only a temporary load. The deflection in metres allowing for load shedding and external live loads is:

Δd = WS
8EI/D3 + ESN/2K

D
WS
8EI/ND3 + ES/2K
WS
8E†3/D3 + 0.4 ES

WALL STRESS

The maximum wall stress around the circumference of a pipe is due to a combination of ring bending under vertical load and arching. At the haunch it is:

ƒ = WS
2†
x (20E†2/D2 + ES )
( 24E†3/D3 + ES )

DURODRAIN® sewer pipes can withstand stresses up to l10MPa (10 x 106 N/m²) since the short term minimum tensile strength is 42MPa and the 50 year nominal strength is 25MPa. Actual strength may be considerably more and depends on stress history.

EXAMPLE: WALL STRESS

ƒ = WS
2†
x (20E†2/D2 + ES )
( 24E†3/D3 + ES )
(6.483 x 103)
(2x0.0092)
x [20 ((1500 x 106) ( 0.00922))/((0.315)2 (3 x IP6))) ]
[24 ((1500 x 106) ( 0.00923))/((0.315)3 +(3x106 ) )]
352 336.9 x
28 590 325.02
3 896 879.96
2 584 997.89
2.584 x 106N/m²
2.584 MPa

DEFLECTION COMPARISON: HD (class 34) vs ND (class 51)

Depth of cover (m) Percentage Deflection
Diameter (mm)
160mm pipe 315mm pipe 500mm pipe
ND HD ND HD ND HD
1 0.586 0.576 0.669 0.658 0.733 0.714
3 1.095 1.076 1.541 1.515 1.738 1.693
6 1.285 1.263 2.181 2.144 2.543 2.477
8 1.313 1.290 2.383 2.342 2.821 2.748
10 1.322 1.299 2.495 2.453 2.988 2.911

The table above compares the percentage deflection between DURODRAIN® normal duty (class 51) and DURODRAIN heavy duty (class 34) of different diameters and depths of cover. A low Es value of 3MPa (clay) was used in the above calculations of pipe deflection.

Note: The deflection of the 160mm normal duty pipe under a 3m soil load is 1.095% compared with 1.076% for heavy duty, a difference of 1.7% in the load bearing capacity, showing that wall thickness has relatively little effect on the soil load bearing capacity. This proves that normal duty (class 51) will adequately do the job of the overdesigned heavy duty (class 34) and result in cost savings.

Effects of Soil Modulus

The table below indicates the effect of soil modulus over deflection for solid wall PVC-U pipe.

Effects of Soil Modulus

DESIGN: VELOCITY AND FLOW

The flow in pipelines, flowing full or partially full but not under pressure, is defined as gravity flow because it is maintained by the slope component of the pipeline, resulting in a hydraulic gradient which is parallel to the pipeline invert. The flow characteristics can be determined by using the adjacent flow chart which is based on Mannings' formula.

Manning's Formula:
V = 1
n
x R0.67S0.5
where V = velocity
n = Manning roughness coefficient (0.008 - 0.010)
R = hydraulic radius, in metres
S = slope, in metres per metres

Velocity and Flow Chart