Drahomír Novák

ENERGETIC-STATISTICAL SIZE EFFECT IN QUASIBRITTLE FAILURE AT CRACK INITIATION

The size effect on the nominal strength of quasibrittle structures failing at crack initiation, and particularly on the modulus of rupture of plain concrete beams, is analyzed. First, an improved deterministic formula is derived from the energy release caused by a boundary layer of cracking (initiating fracture process zone) whose thickness is not negligible compared with beam depth. To fit the test data, a rapidly converging iterative nonlinear optimization algorithm is developed. The formula is shown to give an excellent agreement with the existing test data on the size effect on the modulus of rupture of plain concrete beams. The data range, however, is much too limited; it does not cover the extreme sizes encountered in arch dams, foundations, and retaining walls. Therefore, it becomes necessary to extrapolate on the basis of a theory. For extreme sizes, the Weibull type statistical effect of random material strength must be incorporated into the theory. Based on structural analysis with the recently developed statistical nonlocal model, a generalized energetic-statistical size effect formula is developed. The formula represents asymptotic matching between the deterministic-energetic formula, which is approached for small sizes, and the power law size effect of the classical Weibull theory, which is approached for large sizes. In the limit of infinite Weibull modulus, the deterministic-energetic formula is recovered. Data fitting with the new formula reveals that, for concrete and mortar, the Weibull modulus is approximately equal to 24 rather than 12, the value widely accepted so far. This means that, for extreme sizes, the nominal strength (modulus of rupture) decreases, for two-dimensional (2D) similarity, as the -1/12 power of the structure size, and for 3D similarity, as the -1/8 power (whereas the -1/4 power has been assumed thus far). The coefficient of variation characterizing the scatter of many test results for one shape and one size is shown not to give the correct value of Weibull modulus because the energetic size effect inevitably intervenes. The results imply that the size effect at fracture initiation must have been a significant contributing factor in many disasters (for example, those of Malpasset Dam, Saint Francis Dam and Schoharie Creek Bridge.)

ANN inverse analysis based on stochastic small-sample training set simulation

A new approach of inverse analysis is proposed to obtain parameters of a computational model in order to achieve the best agreement with experimental data. The inverse analysis is based on the coupling of a stochastic simulation and an artificial neural network (ANN). The identification parameters play the role of basic random variables with a scatter reflecting the physical range of potential values. A novelty of the approach is the utilization of the efficient small-sample simulation method Latin Hypercube Sampling (LHS) used for the stochastic preparation of the training set utilized in training the artificial neural network. Once the network has been trained, it represents an approximation consequently utilized to solve the key task: To provide the best possible set of model parameters for the given experimental data. The efficiency of the approach is shown using numerical examples from civil engineering computational mechanics.

FReET: Software for the statistical and reliability analysis of engineering problems and FReET-D: Degradation module

Abstract The objective of the paper is to present methods and software for the efficient statistical, sensitivity and reliability assessment of engineering problems. Attention is given to small-sample techniques which have been developed for the analysis of computationally intensive problems. The paper shows the possibility of “randomizing” computationally intensive problems in the manner of the Monte Carlo type of simulation. In order to keep the number of required simulations at an acceptable level, Latin Hypercube Sampling is utilized. The technique is used for both random variables and random fields. Sensitivity analysis is based on non-parametric rank-order correlation coefficients. Statistical correlation is imposed by the stochastic optimization technique – simulated annealing. A hierarchical sampling approach has been developed for the extension of the sample size in Latin Hypercube Sampling, enabling the addition of simulations to a current sample set while maintaining the desired correlation structure. The paper continues with a brief description of the user-friendly implementation of the theory within FReET commercial multipurpose reliability software. FReET-D software is capable of performing degradation modeling, in which a large number of reinforced concrete degradation models can be utilized under the main FReET software engine. Some of the interesting applications of the software are referenced in the paper.

Size Effect on Flexural Strength of Fiber-Composite Laminates

The size effect on the flexural strength (or modulus of rupture) of fiber-polymer laminate beams failing at fracture initiation is analyzed. A generalized energetic-statistical size effect law recently developed on the basis of a probabilistic nonlocal theory is introduced. This law represents asymptotic matching of three limits: (1) the power-law size effect of the classical Weibull theory, approached for infinite structure size; (2) the deterministic-energetic size effect law based on the deterministic nonlocal theory, approached for vanishing structure size; and (3) approach to the same law at any structure size when the Weibull modulus tends to infinity. The limited test data that exist are used to verify this formula and examine the closeness of fit. The results show that the new energetic-statistical size effect theory can match the existing flexural strength data better than the classical statistical Weibull theory, and that the optimum size effect fits with Weibull theory are incompatible with a realistic coefficient of variation of scatter in strength tests of various types of laminates. As for the energetic-statistical theory its support remains entirely theoretical because the existing test data do not reveal any improvement of fit over its special case, the purely energetic theory-probably because the size range of the data is not broad enough or the scatter is too high, or both.

Structural assessment and reliability analysis for existing engineering structures, theoretical background

The concept presented for the safety assessment of concrete structures integrates nonlinear finite element analysis with stochastic and reliability technology into an advanced engineering tool. The basic aim of the stochastic nonlinear analysis is to calculate the safety index of an existing engineering structure, which characterizes its reliability (and failure probability). The nonlinear solution enables a realistic estimation of the structural response statistics to be obtained (failure load, deflections, cracks, stresses, etc.). The possibility of randomization for such computationally intensive problems is shown. Latin hypercube sampling is used in order to keep the number of required simulations at an acceptable level. Statistical correlation, which is important for a realistic solution, is imposed by using a stochastic optimization technique called simulated annealing. The sensitivity of results to random input parameters can be evaluated using nonparametric rank-order correlation coefficients. The safety index of the analysed structure is calculated from the stochastically obtained structural resistance and expected load distribution using appropriate reliability techniques. The presented approach for the safety assessment of engineering structures supersedes the usual methods based on simplified formulas. It can lead to considerably improved results since the structure is analysed more precisely. Therefore, it supports a higher level of decision-making process in bridge administration and maintenance of transport macrostructure.

Proposal for Standard Test of Modulus of Rupture of Concrete with Its Size Dependence

Recently accumulated test data on the modulus of rupture, as well as analytical studies and numerical simulations, clearly indicate that the flexural strength of concrete, called the modulus of rupture, significantly decreases as the beam size increases. This paper proposes a method to incorporate this size effect into the existing test standards, and focuses particularly on ASTM Standards C 7894 and C 293-94. The proposed method is based on a recently established size effect formula that describes both the deterministic-energetic size effect caused by stress redistribution within the cross section due to finite size of the boundary layer of cracking at the tensile face of beam, and the classical Weibull-type statistical size effect due to the randomness of the local strength of material. Two alternatives of the test procedure are formulated. In the first alternative, beams of only one size are tested (as is recommended in the current standard), and the size effect on the mean modulus of rupture is approximately predicted on the basis of the average of existing information for all concretes. In the second alternative, beams of two sufficiently different sizes are tested. The latter is more tedious but gives a much better prediction of size effect for the concrete at hand; it allows for the estimation of size effect on not only the mean but also the coefficient of variation of the modulus of rupture (particularly, its decrease with increasing size). Numerical examples demonstrate the feasibility of the proposed approach.

Solving Inverse Structural Reliability Problem Using Artificial Neural Networks and Small-Sample Simulation

A new general inverse reliability analysis approach based on artificial neural networks is proposed. An inverse reliability analysis is a problem of obtaining design parameters corresponding to a specified reliability (reliability index or theoretical failure probability). Design parameters can be deterministic or they can be associated with random variables. The aim is to generally solve not only single design parameter cases but also multiple parameter problems with given multiple reliability constraints. Inverse analysis is based on the coupling of a stochastic simulation of the Monte Carlo type (the small-sample simulation method Latin hypercube sampling) and an artificial neural network. The validity and efficiency of this approach is shown using numerical examples with single as well as multiple reliability constraints and with single as well as multiple design parameters, and with independent basic random variables as well as random variables with prescribed statistical correlations.

FraMePID-3PB software for material parameter identification using fracture tests and inverse analysis

Abstract Knowledge regarding the values of fracture-mechanical parameters is critical for the virtual failure modeling of elements and structures made of concrete. A key parameter in nonlinear fracture mechanics modeling is the specific fracture energy of concrete, and its variability. Three-point bending tests on notched-beam specimens are fundamental experiments for the determination of fracture-mechanical parameters. In the present paper, two basic approaches are applied to determine fracture-mechanical parameter values from these tests: (i) the effective crack model/work-of-fracture method, and (ii) inverse analysis using artificial neural networks and stochastic simulations. First, the paper describes suitable methods for the determination of fracture-mechanical parameters. Second, the FraMePID-3PB software tool, which has been developed in order to automate the whole time consuming process of inverse analysis, is described. Finally, the verification of methodology and software is presented using two illustrative examples.

Neural network ensemble-based parameter sensitivity analysis in civil engineering systems

The use of artificial neural networks for parameter sensitivity analysis in civil engineering systems is an emerging research focus of increased interest. Existing methods are generally based on a single neural network, but are inadequate as a basis for parameter sensitivity analysis because of the instability of a single neural network. To address this deficiency, this study develops a neural network ensemble-based parameter sensitivity analysis paradigm. This paradigm features use of a set of preselected superior neural networks to make decisions about parameter sensitivity by synthesizing sensitivity analysis results of individual neural networks. The proposed paradigm is employed to address two classic civil engineering problems: (1) identification of critical parameters in the fracture failure of notched concrete beams and (2) recognition of the most significant parameters in the lateral deformation of deep foundation pits. The results show that tensile strength and modulus of elasticity are the critical parameters in the fracture failure of the notched concrete beam, and elasticity modulus of soil, Poisson’s ratio and soil cohesion are the most significant influential factors in the lateral deformation of the deep foundation pit. The proposed method provides a common paradigm for analysing the sensitivity of influential parameters, shedding light on the underlying mechanisms of civil engineering systems.

Error assessment for wind histories generated by autoregressive method

Abstract This study addresses possible obstacles and errors which can be expected when one applies the autoregressive method for simulation of wind histories. The mean value, variance, and power spectra of the wind speed of the generated sample are assessed by comparison with the target parameters required. The influence of the order of autoregression and of the number of sample points is investigated. A confidence interval probability is used as a measure of the accuracy of the simulation. Numerical results obtained from the example of the wind load on an antenna mast are provided.