Objective This paper establishes a multi-factor strength degradation model of damaged wood members of ancient buildings that changes with time, verifies the applicability of reliability analysis of damaged wood members based on probability density evolution method, so as to improve the calculation accuracy and efficiency of reliability analysis of damaged wood members of ancient buildings, and provide scientific basis for the quantification and evaluation of mechanical properties of members in the protection of ancient buildings.
Method Considering the effects of long-term loading, decay, insect and shrinkage cracking on wood damage, a multi-factor damage time-varying model of wood components was constructed and a strength degradation model was derived with the help of existing models and theories. Typical columns of an ancient timber structure building were used as an example, the influence parameters were determined according to the strength degradation model, the sensitivity of the influence parameters of the damage was calculated and ranked, the key parameters affecting the wood damage were determined by setting the threshold, and the non-key parameters were stabilized to achieve the preliminary dimension reduction of the parameters. 1000 groups of representative points were selected in the parameter domain of key parameters by Latin overshot method. The changing rate of residual strength was calculated based on the intensity degradation model. The probability density evolution equation was constructed according to the probability density conservation, and the joint probability density function of residual strength ratio and random parameters was obtained by the difference method. The probability density function of the residual strength ratio over time was obtained by integrating in the random parameter domain. Finally, the reliability of the component was obtained by integrating the probability density function in the safety domain. At the same time, 10 000 sets of parameter data were randomly sampled by Monte Carlo method to analyze the reliability of the damaged wooden pillar, and the failure probability of the wooden pillar with service time of 1−1000 years was calculated by comparing the two methods
Result With the increase of service time, the damage variable of wooden pillar gradually increased, and the 1 000 groups of members with different parameter values whose service time was 1 000 years almost reached the failure limit. On the probability density evolution surface, the residual intensity ratio with the highest probability decreased gradually. Component failure probability increased with time, which means the reliability decreased. For nodes with service time of 100, 300, 500, 700 and 900 years, the difference of failure probability calculated by Monte Carlo method and probability density evolution method was 9.48%, 3.92%, 6.10%, 8.40% and 4.40%, respectively. Under the premise of more parameter sampling and longer calculation time of Monte Carlo method, the difference of failure probability calculated by the two methods was less than 10%.
Conclusion The multi-factor strength degradation model can be used to evaluate and predict the residual strength of wooden columns, but it still needs further modification. It is feasible to analyze the reliability of damaged wood structures based on probability density evolution method, and compared with Monte Carlo method, probability density evolution method has higher computational efficiency.