Homogenized limit analysis of masonry structures with random input properties: polynomial Response Surface approximation and Monte Carlo simulations

The uncertainty often observed in experimental strengths of masonry constituents makes critical the selection of the appropriate inputs in finite element analysis of complex masonry buildings, as well as requires modelling the building ultimate load as a random variable. On the other hand, the utilization of expensive Monte Carlo simulations to estimate collapse load probability distributions may become computationally impractical when a single analysis of a complex building requires hours of computer calculations. To reduce the computational cost of Monte Carlo simulations, direct computer calculations can be replaced with inexpensive Response Surface (RS) models. This work investigates the use of RS models in Monte Carlo analysis of complex masonry buildings with random input parameters. The accuracy of the estimated RS models, as well as the good estimations of the collapse load cumulative distributions obtained via polynomial RS models, show how the proposed approach could be a useful tool in problems of technical interest.

[1]  Paulo B. Lourenço,et al.  Validation of analytical and continuum numerical methods for estimating the compressive strength of masonry , 2006 .

[2]  G. Apostolakis.  The concept of probability in safety assessments of technological systems. , 1990, Science.

[3]  T. Simpson,et al.  Comparative studies of metamodelling techniques under multiple modelling criteria , 2001 .

[4]  Marvin K. Nakayama,et al.  Techniques for fast simulation of models of highly dependable systems , 2001, IEEE Trans. Reliab..

[5]  J. Sejnoha,et al.  Mesoscopic study on historic masonry , 2008 .

[6]  Alaa Chateauneuf,et al.  Reliability analysis of reinforced concrete grids with nonlinear material behavior , 2006, Reliab. Eng. Syst. Saf..

[7]  Aleš Florian,et al.  An efficient sampling scheme: Updated Latin Hypercube Sampling , 1992 .

[8]  Maurice Lemaire,et al.  Combination of finite element and reliability methods in nonlinear fracture mechanics , 2000, Reliab. Eng. Syst. Saf..

[9]  Francis Tin-Loi,et al.  A simple mixed finite element for static limit analysis , 2006 .

[10]  Jon C. Helton,et al.  Multiple predictor smoothing methods for sensitivity analysis: Example results , 2008, Reliab. Eng. Syst. Saf..

[11]  Donald L. Iglehart,et al.  Importance sampling for stochastic simulations , 1989 .

[12]  Jon C. Helton,et al.  Treatment of Uncertainty in Performance Assessments for Complex Systems , 1994 .

[13]  Jon C. Helton,et al.  Guest editorial: treatment of aleatory and epistemic uncertainty in performance assessments for complex systems , 1996 .

[14]  Paulo B. Lourenço,et al.  Anisotropic Softening Model for Masonry Plates and Shells , 2000 .

[15]  Philip Heidelberger,et al.  A Unified Framework for Simulating Markovian Models of Highly Dependable Systems , 1992, IEEE Trans. Computers.

[16]  S. Sloan,et al.  Upper bound limit analysis using discontinuous velocity fields , 1995 .

[17]  R. Melchers.  Search-based importance sampling , 1990 .

[18]  Gabriele Milani,et al.  Homogenised limit analysis of masonry walls, Part II: Structural examples , 2006 .

[19]  P. Benson Shing,et al.  Interface Model Applied to Fracture of Masonry Structures , 1994 .

[20]  Poul Colberg Olsen.  Rigid-plastic finite element analysis of steel plates, structural girders and connections , 2001 .

[21]  Gian Michele Calvi,et al.  In‐plane seismic response of brick masonry walls , 1997 .

[22]  Jon C. Helton,et al.  Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demanding models , 2009, Reliab. Eng. Syst. Saf..

[23]  Jon C. Helton,et al.  A comparison of uncertainty and sensitivity analysis results obtained with random and Latin hypercube sampling , 2005, Reliab. Eng. Syst. Saf..

[24]  Scott W. Sloan,et al.  A new discontinuous upper bound limit analysis formulation , 2005 .

[25]  Chris J. Pearce,et al.  Discontinuous modelling of masonry bridges , 2003 .

[26]  Antonio Tralli,et al.  Heterogeneous upper-bound finite element limit analysis of masonry walls out-of-plane loaded , 2007 .

[27]  Paulo B. Lourenço,et al.  Homogenization approach for the limit analysis of out-of-plane loaded masonry walls , 2006 .

[28]  M. Elisabeth Paté-Cornell,et al.  Uncertainties in risk analysis: Six levels of treatment , 1996 .

[29]  D. Huntington,et al.  Improvements to and limitations of Latin hypercube sampling , 1998 .

[30]  Hai-Sui Yu,et al.  Lower bound limit analysis of unreinforced masonry shear walls , 2001, Numerical Models in Geomechanics.

[31]  J. C. Helton,et al.  Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty , 1997 .

[32]  Paulo B. Lourenço,et al.  Abbreviated Title : Homogenised limit analysis of masonry , failure surfaces , 2007 .

[33]  Robert L. Winkler,et al.  Uncertainty in probabilistic risk assessment , 1996 .

[34]  Philip Heidelberger,et al.  Fast simulation of rare events in queueing and reliability models , 1993, TOMC.

[35]  Paulo B. Lourenço,et al.  A plane stress softening plasticity model for orthotropic materials , 1997 .

[36]  Perwez Shahabuddin,et al.  Importance sampling for the simulation of highly reliable Markovian systems , 1994 .

[37]  F. O. Hoffman,et al.  Propagation of uncertainty in risk assessments: the need to distinguish between uncertainty due to lack of knowledge and uncertainty due to variability. , 1994, Risk analysis : an official publication of the Society for Risk Analysis.

[38]  Timothy W. Simpson,et al.  Metamodels for Computer-based Engineering Design: Survey and recommendations , 2001, Engineering with Computers.

[39]  C. T. Haan.  Parametric Uncertainty in Hydrologic Modeling , 1989 .

[40]  Gabriele Milani,et al.  3D homogenized limit analysis of masonry buildings under horizontal loads , 2007 .

[41]  P. C. Olsen.  Evaluation of triangular plate elements in rigid-plastic finite element analysis of reinforced concrete , 1999 .

[42]  Jon C. Helton,et al.  Multiple predictor smoothing methods for sensitivity analysis: Description of techniques , 2008, Reliab. Eng. Syst. Saf..