Probabilistic procedure for design of untreated timber poles in-ground under attack of decay fungi

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Abstract

Based on first-order probability theory, this paper presents a probabilistic procedure for design of timber poles in ground contact under attack of decay fungi. Fungal attack prediction model developed in a multi-disciplinary national project in Australia, sponsored by the Forestry and Wood Products Research and Development Corporation, is used in this study for decay progress modelling. A durability design factor, kD, is derived and proposed for consideration in practical design of timber construction. Examples for computation of kD for untreated timber poles installed at two sites in Australia are given.

Introduction

The design and analysis of a timber construction has conventionally ignored the effect of material degradation over its service life. In the past destructive events, however, a significant number of wood houses that either collapsed or were heavily damaged, such as those found after the 1994 Northridge, California, and the 1995 Kobe, Japan, earthquakes, were found to have bio-deteriorated wood members (e.g. [1]). The negligence of the effect of material-aging processes on structural performance, therefore, has led to unexpected structural failures when the wood elements were subject to degradation due to inappropriate use of the construction, incorrect detailing, or deficient construction procedures.

The timber engineering design codes in Australia follow similar design philosophy that excludes the effect of material degradation. This paper proposes a durability factor, defined as kD, to take into account the effect of material deterioration. For example, making use of the Australian Standard 1720.1–1997 [2], the bending strength capacity Mu for timber elements may be given byMu=kDk1k2k3,,Zinfk,where Zin denotes the initial section modulus, fk denotes the characteristic bending strength of the material, and ki,i=1,2,3,, denotes the modification factor for stability, duration of loading, moisture, etc.

In the following, the field test of small clear stakes attacked by fungal decay is described, followed by a discussion on the processing of data obtained from these stakes to obtain the mean and variability of decay depth of wood stakes and subsequently the strength parameters of timber poles. These parameters are then used to obtain the durability factor kD for untreated timber poles.

Section snippets

Background

To investigate the natural durability of wood in Australia, use was made of data obtained from field tests of small clear stakes conducted by the former Division of Forest products, CSIRO, at five sites in eastern and southern Australia over the period of 1968–2004, giving a test period of around 35 yr [3]. The five sites are located at: (1) Walpeup, Victoria; (2) Melbourne, Victoria; (3) Sydney, New South Wales; (4) Brisbane, Queensland; and (5) Innisfail, Queensland. Details of the setup of

Median decay rates of stakes

For engineering purposes, the commercially used species have been classified into four natural durability classes with class 1 being the most durable and class 4 the least durable, as defined in the Australian Standard AS 5604 [5].

The data at each site was processed to obtain median decay depth for each class of timber, taking into account the fact that the data sets were truncated since some stakes were either lost or totally decayed in less than 35 yr. As an example of the data obtained, Fig. 1

Variability of decay of stakes

The data from the field tests was processed to obtain an estimate of the uncertainties associated with the use of the model described in Appendix A. To do this, lognormal and two-parameter Weibull distributions were fitted to the data. From this it was found that the uncertainties associated with kwood, denoted by a coefficient of variation (COV), Vwood, was about 0.45, 0.55, 0.75, and 0.90 for timber of durability classes 1, 2, 3, and 4, respectively. Similarly the uncertainty associated with k

Decay of untreated de-sapped timber poles

It is normally assumed that decay of a timber pole occurs on a cross-section that is 100–200 mm below the ground line. In the following, it will be assumed that this decay progresses inwards from the perimeter as shown in Fig. 4.

At the decayed cross-section, the perimeter of a timber pole could be considered as a combination of N ‘imaginary’ wood stakes, as illustrated schematically in Fig. 5. Two plausible scenarios (among many) for the progress of decay of these N stakes are as follows. In the

Mean pole strength

At time zero, the bending strength of a round pole, R0, is given byR0=π32D3fult,where D is the initial diameter (mm) and fult is the ultimate fiber strength of undecayed wood (MPa). If attack by decay fungi occurs, then in accordance with the above assumption, after time t the bending strength, denoted by Rt, becomes:Rt=π32(D-2dt)3fult,where dt is the decay depth (mm) at time t.

Considering that the decay depth dt is a random variable, the bending strength at time t is also a random variable.

Variability of pole strength

In accordance with the scenario 2 in Section 5, the variance of strength at time t, denoted by σR,t2, is given by a first-order approximation:σR,t2(Vdd¯t)2(Rtdt|dt=d¯t)2=[3π16fultVdd¯t(D-2d¯t)2]2,where d¯t is an estimate of mean value of decay depth at time t, and Vd denotes the uncertainty of decay due to timber properties. The uncertainty parameter Vd will be taken to be a COV defined byVd=Vwood2+Vclimate2+Vmodel2,where Vwood and Vclimate have been defined in Section 4, and Vmodel allows

Probability-based durability factor

Using the approximation discussed by Ravindra and Galambos [7], the acceptable design strength Rdesign can be approximated byRdesign=kcomRmeanexp(-0.6βVR),where kcom, an arbitrary factor applied to both load and strength specifications; Rmean, mean value of R; VR, COV of R; β, safety index.

A durability factor kD will be defined bykD=Rdesign,tRdesign,0,where Rdesign,0, initial design strength; Rdesign,t, design strength at time t.

Then from Eq. (10) we obtain:Rdesign,0=kcomRmean,0exp(-0.6βVR,0),R

Worked examples

As an illustration for service-life estimation of structural timber, consider round poles with a diameter of 350 mm, made from de-sapped hardwood of durability classes 2 and 3 without preservative treatment and applications of maintenance procedures. The timber poles are assumed to be installed at two sites. One is at Innisfail, Queensland, a hot and wet site representing a favourable condition for decay fungi, and the second is at Walpeup, Victoria, a temperate and dry site representing a harsh

Concluding comment

This paper presents a probabilistic approach for the structural design of timber poles subjected to attack of decay fungi. The decay prediction model provides a method of quantifying the effects of durability for engineering purposes. For this purpose, a durability factor kD has been developed and proposed to be included in the design procedures for timber construction. For example, comparing Fig. 6, Fig. 7 shows that after 20 years the kD factor for class-2 timber would be about 0.85 for a

Acknowledgments

Development of the in-ground decay model and the design procedure was part of an Australian national project on design for durability of timber construction funded by the Forest and Wood Products Development Corporation, Australia.

References (7)

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