On the use of NDT data for reliability-based assessment of existing timber structures

Published Date
November 2013, Vol.56:298–311, doi:10.1016/j.engstruct.2013.05.014

Author 

Hélder S. Sousa ^a,,

John D. Sørensen ^b,

Poul H. Kirkegaard ^b,

Jorge M. Branco ^a,

Paulo B. Lourenço ^a,

aDepartment of Civil Engineering, ISISE, University of Minho, Portugal

bDepartment of Civil Engineering, Aalborg University, Denmark

Received 11 January 2013. Revised 7 April 2013. Accepted 7 May 2013. Available online 6 June 2013.

Highlights

• •
  Framework for reliability-based assessment of timber structures using NDT.
• •
  Updating deterioration models in chestnut timber elements by Bayesian methods.
• •
  Use of different prior information and uncertainty levels for reliability assessment.
• •
  Importance of key elements is investigated in different structural systems.
• •
  Determination of reliability indicators.

Abstract

The objective of this paper is to address the possibilities of using non-destructive testing (NDT) data for updating information and obtaining adequate characterization of the reliability level of existing timber structures and, also, for assessing the evolution in time of performance of these structures when exposed to deterioration. By improving the knowledge upon the mechanical properties of timber, better and more substantiated decisions after a reliability safety assessment are aimed at.

Bayesian methods are used to update the mechanical properties of timber and reliability assessment is performed using First Order Reliability Methods (FORM). The results show that different degrees of belief in the updating data may significantly influence the reliability level. The updating data to be used are NDT results obtained with ultrasound, resistance drilling and pin penetration equipments. The tests were conducted on chestnut wood (Castanea sativa Mill.) specimens, and were combined with tests to determine the compressive strength parallel to the grain. The uncertainty of the different NDT results is modeled by Maximum Likelihood estimates. Resistance distributions functions are considered to analyze the difference before and after updating by NDT, showing that lower variations may typically be obtained with the new information. Moreover, updating of the parameters in different deterioration models is considered in order to be able to evaluate the time dependency of the reliability, and information of NDT is also used to calibrate these models.

The proposed approach is used for reliability assessment of different structural timber systems. Reliability of the structural system is assessed regarding the failure consequences of individual elements defined as key elements which were determined by their influence on the cross section loss. The results given by the pin penetration tests were the most similar to the reference experimental model with statistic parameters given by the results of destructive tests. The resistance drilling and ultrasound updating schemes led to higher level of reliability than the reference model values, therefore these updating data should be considered with caution, as they can result in unsafe results for the reliability compared to the reference models.

Keywords

Timber structures

NDT

Assessment

Reliability

Updating methods

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Nomenclature

Latin upper case letters

A

area

COV

coefficient of variation

DT

destructive tests

E

expected value

E_dyn

dynamic modulus of elasticity

G

permanent load

G_k

characteristic value for permanent load

M_i

safety margin

NDT

non-destructive testing

probability of failure of a parallel system

probability of failure of a series system

Q

variable load

Q_k

characteristic value for variable load

R

resistance function

RM

drilling resistance indicator

X

stochastic variable

Latin lower case letters

a

square cross section size

b

width

f_c,0

compressive strength parallel to grain

f_m

bending strength

f_m,k

characteristic bending strength

f_N( )

likelihood function

( )

prior density function

( )

posterior density function

f_X( )

density function

g

limit state equation

g_i( )

failure function

h

height

k_climate

parameter of climate conditions

k_mod

modification factor

k_wood

parameter of timber durability class

l

length

m

sample mean

m′

prior function hypothetical sample average

posterior function hypothetical sample average

n

number of tests

n′

prior function hypothetical number of observations for m′

posterior function hypothetical number of observations for m′

p_f

probability of failure

q

vector of distribution parameters

r

penetration rate

s

sample standard deviation

prior function hypothetical sample value

posterior function hypothetical sample value

central t-distribution value

t_lag

time between construction and the point that noticeable decay commences

ν′

prior function hypothetical number of degree of freedom for s′

posterior function hypothetical number of degree of freedom for s′

sample of realizations

Greek lower case letters

α

factor for modeling the fraction of variable load

α_i

regression parameter

β

reliability index

γ_G

partial safety factor for permanent loads

γ_m

partial safety factor for material properties

γ_Q

partial safety factor for variable loads

ε

lack-of-fit

λ

failure rate

λ_rel

slenderness ratio

μ

mean value

μ_depth

average of pin penetration tests

μ_DT

average of destructive tests

μ_Edyn

average of ultrasound tests

μ_RM

average of resistance drilling tests

σ

standard deviation

τ

perimetral loss of cross-section

Fig. 1.

 Table 1

Table 1.

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Fig. 4.

 Table 2

Table 2.

Fig. 5.

Fig. 6.

Fig. 7.

Fig. 8.

 Table 3

Table 3.

Fig. 9.

Fig. 10.

Fig. 11.

 Table 4

Table 4.

Fig. 12.

Fig. 13.

Fig. 14.

 Table 5

Table 5.

Fig. 15.

Fig. 16.

Fig. 17.

• ⁎ 
  Corresponding author. Address: ISISE, University of Minho, Department of Civil Engineering, Azurém, 4800-058 Guimarães, Portugal. Tel.: +351 253510200; fax: +351 253510217.

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