Cost Effectiveness of HDPE Sheathing For Post-Tensioned Prestressed Concrete Structures Over Galvanised Metallic Ducts – A Study

S.G. Bapat, Chief Engineer (Civil-Designs) Retd; Mr. Arvind Shrivastava, Addl. Chief Engineer (Civil) Nuclear Power Corporation of India Ltd. Mumbai, and Mr. Umesh K. Rajeshirke, Spectrum Consulting Engineers, Navi Mumbai.

Introduction

Prestressing duct is one of the vital elements of total prestressing system.

The main functions of the duct are:

• To create cavity / void in the concrete, along the profile of the prestressing cable so that the cable can be threaded into it after the concrete gets hardened.
• To provide the protection against the corrosion to the prestressing steel.

Different types of ducts are available and they can be classified depending upon their surface profile, such as plain or corrugated, and depending on the material from which these ducts are manufactured, such as metallic or non-metallic.

Metallic ducts made from steel strips with corrugations are being used over long period for bonded post tensioning tendons. Plastic ducts have been used for many years in the industry, but mostly in the form of smooth pipes for applications involving unbounded cables like external prestressing, ground anchors etc. Only recently, the corrugated thick-walled HDPE (High Density Polyethylene) ducts have become popular internationally for other applications of post-tensioned tendons like bridges etc. They offer excellent features over metallic sheathing such as improved corrosion protection of the tendons, reduced friction losses during stressing of the tendons, increased fretting fatigue resistance of the tendon, their feasibility for corrosion monitoring and the durability of the ducts themselves. Many times it is found that, when there is large time gap between the concreting of the structure and prestressing operations, the metallic duct gets corroded and then leads to a major problem of leakage of grout from one duct to the adjacent ducts. This problem can be completely avoided if the HDPE ducts are used.

The cost of corrugated plastic ducts for bonded post-tensioning was strongly influenced by the production method. These ducts were typically produced by extrusion & then spiral winding process requiring significant investment. Since they were produced in relatively small quantities, corrugated plastic ducts for bonded post tensioning system were typically more expensive, by 15–20% higher when compared with corrugated thin walled steel ducts till late 2000. But with era of enormous use of PE ducts in large quantities coupled with modern speedy processing methods, made PE ducts very competitive since then. The price gap further became not only narrow but also made metallic ducts costly due to skyrocketing prices of metallic strips since 2002. The PE ducts since then are becoming very competitive & cost effective than metallic ducts. Ducts represent about 5% of the total post-tensioning cost, which is about 10% of total construction cost of a bridge structure.

In addition, significant improvement of durability and quality of the main reinforcement of a structure can be achieved. Long tendons with significant friction losses due to tendon deviations will benefit from the reduced friction coefficient of PE ducts and show an economy due to a more effective use and therefore, a reduction of the required amount of prestressing steel leading to an overall economy of the structure. The value of prestressing force available at a particular section of the structure (e.g. superstructure of the bridge) to resist the tensile stresses depends on the loss in the cable force due to friction between the cable and duct during stressing operation. If the coefficient of friction is small, more is the force available and less is the prestressing steel required. This results in saving in cost, especially for the structures like long span bridges, continuous and curved girders, prestressed concrete silos, water tanks, pipe lines, etc.

This report aims at providing a quantitative assessment of the cost saving in prestressing system for some of the typical prestressed concrete structures.

The theoretical background on loss in cable force due to friction between cable and duct is presented followed by the losses due to wobble of duct. The case studies are presented, which are simply supported I girders for various spans, box girders, continuous box girder, simply supported curved box girders and continuous curved box girders.

Theoretical Background

The physical phenomenon of frictional loss of a cable around a curve is well known [1]. For a ready reference, a derivation for the same is given below.


Curvature Effect: Consider an infinitesimal length dx of a prestressing tendon which follows the arc of a circle of radius R, (Ref. Fig. 1). Then the change in angle of the tendon along its length dx is

dα = dx / R

For this infinitesimal length dx, the force in the tendon may be considered constant and equal to F; then the normal component of pressure N produced by the force F bending around an angle dα is given by

N = Fdα = Fdx / R

The amount of frictional loss dF around the length dx is given by the pressure times a coefficient of friction µ, thus,

dF = -µN
dF = -µFdx / R = -µFdα

Transposing, we get

dF / F = -µdα

Integrating this on both sides, we have

log_eF = -µα -----------(1)

Using the limits F₁ and F₂, we have the conventional friction formula

F₂ = F₁e^-µα = F₁e^-µL/R

Since α = L/R for a section of constant R.

For tendons with a succession of curves of varying radii, it is necessary to apply this formula to the different section in order to obtain the total loss.

Wobble effect: Wobble coefficient, b depends physically on the rigidity of the duct which mainly depends on the duct diameter and the intermediate supports provided while laying the duct. Typically, the value varies from 0.5^o / m for smaller ducts to 0.3^o / m for big stiff ducts. The wobble effect can also be directly expressed in term of length using parameter K, which is K = bµ. To compute frictional loss due to wobble or length effect, KL can be substituted for ìá in formula 1, and then we have,

Log_eF = -KL F₂ = F₁e^-KL

If the length and curvature effects are combined, we get

Log_eF = -µα -KL

For limits F₁ and F₂,

F₂ = F₁e^-µα-KL

Or, in terms of unit stresses,

ƒ₂ = ƒ₁e^-µα-KL


The friction loss is obtained from this expression. Loss of prestress is given as FR = F₁ – F₂. The stress in cable at the jacking end is ƒ₁, and length to the point is L where the stress is ƒ₂, (Ref. Fig 2) Then,

FR = ƒ₁ – ƒ₂ = ƒ₁ - ƒ₁e^-µα-KL = ƒ1 (1 - e^-µα-KL) --------------(2)

Case Studies

Equation (2) shows the influence of µ on the net effective prestressing force available for resisting the externally applied forces. Lower the value of the µ, higher is the prestressing force available and less is the prestressing steel required. To assess the extent of this benefit, four case studies are carried out, the summary of which is presented in following sections.

The cost comparison is made between the conventional bright metal sheathing and the HDPE sheathing. In case of HDPE, two sets of values for µ & k are used, first is based on the values specified in IRC-18 [2] and other is based on average value specified in fib bulletin No. 7 [2].

Girder Bridges

For this study the standardized design of the girders of various spans viz. 30, 35, & 40 ms published by MoST [4] are used as the base design, i.e. the same cable profile, number of cables, type of cables are used for the comparison.

In MoST design, the number of cables and their profile is arrived at using µ & K values of bright metal sheathing which are 0.25 and 0.0046 respectively. In this study, it is tried to find out that what could have been the reduction in cable/strands if the HDPF sheathing would have been used instead of white metal sheathing. Brief calculations are presented in Table No. 1 to 3 for girders with span of 30, 35, & 40 m respectively and summary of the results are tabulated below:

It can be seen that the saving in prestressing steel is of the order of 6.25 to 7.3% for span of 40 m by just changing the white metal sheathing to HDPE sheathing.

Box Girder (Simply Supported)

Similar study has been carried out for box girders with different spans. The results are presented in table No. 4 through 8 for 30, 35, 40, 45 & 50 m spans respectively. The table below gives the summary of the results:

Box Girder (Continuous Over 3 Spans)

Three span continuous box girder with span arrangement of 40m + 40m + 40m has been considered for this case. For the comparison, longest cable in the girder which is running from one end to the other is selected. The profile of this cable is shown in Fig. 3. The loss in prestressing force is worked out at midpoint of cable i.e. center of the middle span. (The cables are to be stressed from both the ends.)


The change in angle from the stressing end to the mid point of cable = 96.93° and cumulative length upto this point is 60.87 m. Hence the available prestressing force at the mid point and saving in prestressing steel considering various values of µ & k is given below,

Of course not all the cables in the girder will be having similar profile and length. Some of the cables run locally over short distance having lesser change in angle having different values of prestressing force available. The overall saving in prestressing steel for the girder is found to be about 14 to 16 % i.e. about 4.8 t, which in terms of cost is about Rs.3,60,000/- (Assuming Rs.75,000.0 / t, which includes the cost of installation, stressing, grouting, etc. complete)

Continuous Box Girder With Curvature in Plan

Similar study has been carried out for continuous curved box girder having similar span arrangement i.e. 40m +40m +40 m and the same cable profile in elevation. The radius of curvature, in plan, is 60 m. Again for the comparison, longest cable in the girder which is running from one end to the other is selected. The losses in prestressing force is worked out at midpoint of cable i.e. center of the middle span & the cable is to be stressed from both the ends.

The change in angle from the stressing end to the mid point of cable = 136.4° and cumulative length, up to this point is 60.9 m. the available prestressing force at the mid point and saving in prestressing steel, considering for various values of m & k, is given below,

Again not all the cables in the girder will be having similar profile and length. Some of the cable may run locally over short distance having lesser change in angle and having different values of effective prestressing force available. The overall saving in prestressing steel for the girder is found to be about 16 to 18 % i.e. about 6.25 t, which in term of cost is Rs. 4,68,750/-

Conclusion

The main benefit of using HDPE ducts in prestressing system is the enhancement in the durability of the prestressed concrete structure. It renders the excellent protection of the prestressing steel, the most important element contributing to the safety of the structure against the corrosion. The users may get this benefit at more of less the same cost of conventional metal sheathings.

Due to the lesser value of friction & wobble co-coefficients, the HDPE sheathing offers overall economy in prestressing system. This was an attempt made to quantify and bring out this advantage with the help of few case studies. This would give rough idea to the user about the possible saving in overall cost of the structure. The cost benefit increases with span of the girder. In addition to cost benefit, other advantages are user & friendly (i.e. easy to handle and joining), high durability etc. this, indeed, makes HDPE corrugated sheathing an ideal material in prestressing industry.

A word of caution is necessary while describing and specifying the raw material to be used in the manufacture of plastic ducts. Absolute care should be taken not to allow PVC (Polyvinyl chloride) as the material. The reason being that PVC, when exposed to heat or fire, is likely to give out chlorine gas and/or hydrochloric acid. In fact, the formation of these two hazardous substances, namely chlorine gas and hydrochloric acid, occurs even at a temperature of about 70°C when exposed to weather. In case of high strength concrete, concrete temperatures are reaching upto 70°C due to heat of hydration. Obviously, the presence of chlorine and/or hydrochloric acid is extremely corrosive and detrimental to steel & concrete structures. Also these two substances are environmentally most damaging. Thus care should be taken to ascertain that the prestressing ducts are not made of PVC.

References

• Prestressed Concrete Structure by T Y Lin
• fib Bulletin No. 7: Technical Report on Corrugated plastic duct for internal
• bounded post-tensioning, June 2000
• IRC:18-2000: Design Criteria for Prestressed Concrete Road Bridges (Post-Tensioned Concrete)
• Standard Drawings for Road Bridges by MoST, 1990