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Friday, 2 December 2016

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

  • Nomenclature

    Latin upper case letters

    A
    area
    COV
    coefficient of variation
    DT
    destructive tests
    E
    expected value
    Edyn
    dynamic modulus of elasticity
    G
    permanent load
    Gk
    characteristic value for permanent load
    Mi
    safety margin
    NDT
    non-destructive testing
    probability of failure of a parallel system
    probability of failure of a series system
    Q
    variable load
    Qk
    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
    fc,0
    compressive strength parallel to grain
    fm
    bending strength
    fm,k
    characteristic bending strength
    fN( )
    likelihood function
    ( )
    prior density function
    ( )
    posterior density function
    fX( )
    density function
    g
    limit state equation
    gi( )
    failure function
    h
    height
    kclimate
    parameter of climate conditions
    kmod
    modification factor
    kwood
    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′
    pf
    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
    tlag
    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
    αi
    regression parameter
    β
    reliability index
    γG
    partial safety factor for permanent loads
    γm
    partial safety factor for material properties
    γQ
    partial safety factor for variable loads
    ε
    lack-of-fit
    λ
    failure rate
    λrel
    slenderness ratio
    μ
    mean value
    μdepth
    average of pin penetration tests
    μDT
    average of destructive tests
    μEdyn
    average of ultrasound tests
    μRM
    average of resistance drilling tests
    σ
    standard deviation
    τ
    perimetral loss of cross-section
    Fig. 1.
     Table 1
    Table 1.
    Fig. 2.
    Fig. 3.
    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.

    For further details log on website :
    http://www.sciencedirect.com/science/article/pii/S0141029613002289
    Posted by A. Haikal at 9:19:00 am
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