Showing papers in "Journal of Engineering Mechanics-asce in 1990"
TL;DR: A fast and accurate method of generating realizations of a homogeneous Gaussian scalar random process in one, two, or three dimensions is presented, motivated first by the need to represent engineering properties as local averages and second to be able to condition the realization easily to incorporate known data or change resolution within sub‐regions.
Abstract: A fast and accurate method of generating realizations of a homogeneous Gaussian scalar random process in one, two, or three dimensions is presented. The resulting discrete process represents local averages of a homogeneous random function defined by its mean and covariance function, the averaging being performed over incremental domains formed by different levels of discretization of the field. The approach is motivated first by the need to represent engineering properties as local averages (since many properties are not well defined at a point and show significant scale effects), and second to be able to condition the realization easily to incorporate known data or change resolution within sub‐regions. The ability to condition the realization or increase the resolution in certain regions is an important contribution to finite element modeling of random phenomena. The Ornstein‐Uhlenbeck and fractional Gaussian noise processes are used as illustrations.
490 citations
TL;DR: In this article, a particle model for brittle aggregate composite materials such as concretes, rocks, or ceramics is presented, which is also applicable to the behavior of unidirectionally reinforced fiber composites in the transverse plane.
Abstract: A particle model for brittle aggregate composite materials such as concretes, rocks, or ceramics is presented. The model is also applicable to the behavior of unidirectionally reinforced fiber composites in the transverse plane. A method of random computer generation of the particle system meeting the prescribed particle size distribution is developed. The particles are assumed to be elastic and have only axial interactions, as in a truss. The interparticle contact layers of the matrix are described by a softening stress‐strain relation corresponding to a prescribed microscopic interparticle fracture energy. Both two‐ and three‐dimensional versions of the model are easy to program, but the latter poses, at present, forbidding demands for computer time. The model is shown to simulate realistically the spread of cracking and its localization. Furthermore, the model exhibits a size effect on: (1) The nominal strength, agreeing with the previously proposed size effect law; and (2) the slope of the post‐peak l...
487 citations
TL;DR: In this paper, the probability of the parabolic failure domain is computed exactly by inversion of the characteristic function for the Parabolic quadratic form, and the exact results for the probability content of the failure domain obtained from the full second-order Taylor expansion of a failure function at the design point are presented.
Abstract: In second-order reliability methods the failure surface in the standard normal space is approximated by a parabolic surface at the design point. The corresponding probability is computed by asymptotic formulas and by approximation formulas. In this paper the probability content of the parabolic failure domain is computed exactly by inversion of the characteristic function for the parabolic quadratic form. Also, the exact results for the probability content of the failure domain obtained from the full second-order Taylor expansion of the failure function at the design point is presented. The approximating parabola does not depend on the formulation of the failure function as long as this preserves the original failure surface. This invariance characteristic is in general not shared by the approximation obtained using the full second-order Taylor expansion of the failure function at the design point. The exact results for the probability content of the approximating quadratic domains significantly extend the class of problems that can be treated by approximate methods.
288 citations
TL;DR: In this paper, a constitutive model for sand is formulated within the general framework of bounding surface hypoplasticity, which can simulate different features of sand behavior under loading conditions, which range from simple monbtonic to complex cyclic at different amplitudes and directions.
Abstract: A comprehensive constitutive model for sand is formulated within the general framework of bounding surface hypoplasticity. The distinctive feature of this model is the dependence of the loading and plastic strain rate directions on the stress rate direction. This property renders the model hypoplastic. The model can simulate different features of sand behavior under loading conditions, which range from simple monbtonic to complex cyclic at different amplitudes and directions. In particular, the successful simulation of the response under “rotational shear” is one of the distinctive properties of the model, and it is mainly due to its hypoplastic character. The importance of such predictive capability in practice is related to the phenomenon of liquefaction, which may occur under such cyclic loading conditions of a complex nature, entailing cyclic changes of both principal stress values and principal stress directions. The paper presents a step‐by‐step calibration procedure of the different constants and a...
279 citations
TL;DR: In this article, a generalized microplane model was developed to describe tensile cracking and nonlinear triaxial response of brittleplastic materials in compression and shear, which was implemented in a 3D model.
Abstract: A generalized microplane model, which was previously developed to describe tensile cracking and nonlinear triaxial response of brittleplastic materials in compression and shear, is implemented in a
250 citations
TL;DR: In this paper, the implication and limitation of scalar damage models are analyzed, in particular, the elastic damage thermodynamic potential and the effective stress concept are reexamined, and the notion of isotropic and anisotropic damage variables in continuum damage mechanics is discussed.
Abstract: The present work analyzes the implication and limitation of some scalar damage models. In particular, the elastic‐damage thermodynamic potential and the effective stress concept are reexamined. It is demonstrated that isotropic damage does not necessarily imply scalar damage representation in general. The notion of isotropic and anisotropic damage variables in continuum damage mechanics is then discussed. In addition, some results from micromechanical analyses are applied to show the direct relationship between the fourth‐order damage tensor and the damage‐induced compliance tensor characteristic of microcrack‐weakened brittle materials. It is shown that even for isotropic damage one should employ an isotropic fourth‐order damage tensor (not a scalar damage variable) to characterize the state of damage in materials, in accordance with the effective stress concept. In general, however, a damage tensor is anisotropic and should be derived from micromechanical analysis when possible.
227 citations
TL;DR: In this paper, a mechanistic approach to constitutive modeling of asphalt concrete under complicated repetitive loading conditions with rest periods is presented, based on an extensive literature review of the literature.
Abstract: This paper presents a mechanistic approach to constitutive modeling of asphalt concrete under complicated repetitive loading conditions with rest periods. From an extensive literature review, two m...
203 citations
TL;DR: In this paper, a combined plasticity and damage mechanics model for concrete is developed within the general framework of the internal variable theory of thermodynamics, and the necessity of using both plasticities and damage is emphasized.
Abstract: A combined plasticity and damage mechanics model for concrete is developed within the general framework of the internal variable theory of thermodynamics. The necessity of using both plasticity and...
195 citations
TL;DR: In this paper, the prediction of the expected vortex-induced response of flexible bridges is treated as a two-step process, in the first step, the parameters of a mathematical model, used to describe the response of a rigid, elastically mounted, scaled section model of a bridge are identified A technique for estimating these parameters using wind-tunnel test results is proposed in the second step, model parameters are used in the equation of motion of the prototype bridge to obtain its response.
Abstract: One of the recurring aerodynamic concerns of both existing and projected new and flexible bridges, typically those of long span, is the possibility that the deck may be set into periodic oscillation by cross winds of relatively low velocity This general phenomenon, regardless of the specific details of the local flow about the structures, has been termed “vortex‐induced oscillation” In this paper, prediction of the expected vortex‐induced response of flexible bridges is treated as a two‐step process In the first step, the parameters of a mathematical model, used to describe the response of a rigid, elastically mounted, scaled section model of a bridge are identified A technique for estimating these parameters using wind‐tunnel test results is proposed In the second step, model parameters are used in the equation of motion of the prototype bridge to obtain its response A method that accounts for the effect of imperfect spanwise correlation of aerodynamic forces on flexible‐bridge response, based on m
169 citations
TL;DR: In this paper, the pullout of a single fiber from a brittle matrix is widely recognized as one of the basic tests to be performed to provide information about the expected behavior of a given fiber-reinforced brittle matrix composite material.
Abstract: The pullout of a single fiber from a brittle matrix is widely recognized as one of the basic tests to be performed to provide information about the expected behavior of a given fiber-reinforced brittle matrix composite material. Thus, it is of great importance that the pullout test be interpreted in a way that yields the true material parameters. Two approaches to the fiber/matrix debonding problem can be made: (1) The stress approach where the criterion for growth of the debonded fiber/matrix interface is expressed in terms of the interfacial stress; and (2) the fracture mechanical approach where the criterion for interfacial debonding is expressed in terms of energy equilibrium. This paper investigates these two approaches by applying both to the same model, which includes frictional stresses on the debonded interface. The debonding load-versus-crack length relationships predicted by the two approaches are compared and differences in the parametric dependency are discussed. The results predicted by the fracture mechanical approach are compared with available experimental results.
145 citations
TL;DR: In this paper, a series of conventional triaxial tests on fully saturated and partly saturated specimens is performed to study regions of stable and unstable behavior, showing that during drained conditions, stress paths directed in the region where Drucker's postulate is violated do not produce unstable behavior.
Abstract: According to Drucker's postulate, materials should become unstable when the second increment of plastic work is negative. A series of conventional triaxial tests on fully saturated and partly saturated specimens is performed to study regions of stable and unstable behavior. Experiments on specimens exhibiting dilation or compression show that, during drained conditions, stress paths directed in the region where Drucker's postulate is violated do not produce unstable behavior. However, for specimens that compress and have degrees of saturation higher than critical, there is a change in drainage conditions causing the stress path to be directed within the region where plastic loading occurred with a negative second increment of work and instability. Previously stated stability conditions for materials with nonassociated flow are analyzed in view of the experimental results on saturated and partly saturated sands.
TL;DR: In Cartesian coordinates importance sampling has been shown to be remarkably effective in improving the efficiency of Monte Carlo simulation techniques for reliability calculations in structural engineering as discussed by the authors, and this technique has been used in many applications.
Abstract: In Cartesian coordinates importance sampling has been remarkably effective in improving the efficiency of Monte Carlo simulation techniques for reliability calculations in structural engineering. T...
TL;DR: In this article, the stiffness tensor relating the stress and strain in the generalized Hooke's law can take various forms depending upon the symmetry of the mechanical properties of the granular material.
Abstract: The stiffness tensor relating the stress and strain in the generalized Hooke's law can take various forms depending upon the symmetry of the mechanical properties of the granular material. This material symmetry is expected to be closely related to the packing structure of the granular material. In this paper, the microstructural continuum method is employed to study the relationship between the symmetry of mechanical properties and the packing structure for random granular packings. The distribution density functions characterizing the packing structure are represented by spherical harmonics expansion. Closed‐form solutions for the stiffness tensor are derived for anisotropic granular packings of equal spheres with linear interparticle contact interactions. The relation between the “fabric” parameters describing the density functions and the material symmetry are discussed. Bounds imposed by the condition of positive definiteness of strain energy on fabric parameters are also studied. Parametric study is...
TL;DR: In this article, the authors extended the fictitious crack model to include the effect of crack shearing, and the existence of multiple cracks is considered, and a consistent theory for unloading and possible closure of the cracks is presented.
Abstract: he fictitious crack model is extended so that it includes the effect of crack shearing. By the introduction of the so-called equivalent length, it is possible to establish a smeared version of the fictitious crack model. The equivalent length is a purely geometrical quantity that depends entirely on the size and form of the element and on the crack direction. A realistic modeling of crack shearing is obtained, and the smeared constitutive relations are objective with respect to both loading normal to the crack plane and loading tangential to the crack plane. The existence of multiple cracks is considered, and a consistent theory for unloading and possible closure of the cracks is presented. FE calculations of a concrete specimen using four different element types demonstrate the objectivity of the theory even when distorted meshes are used. (Less)
TL;DR: In this paper, the experimental results obtained from the study of two similar cylindrical water tanks are presented from the case where one of the tanks was directly fixed to the earthquake simulator, the other was mounted on the base of a scaled nine-story steel structure.
Abstract: This paper presents the experimental results obtained from the study of two similar cylindrical water tanks. One of the tanks was directly fixed to the earthquake simulator, the other was mounted on the base of a scaled nine‐story steel structure. The structure was isolated on eight multilayered elastomeric bearings. Due to the reduction in the ground accelerations, the dynamic pressure is reduced for the tank in the isolated structure. Free‐surface water elevation was slightly increased due to the lower frequency that characterizes the motion of base‐isolated structures. This problem can be overcome by appropriate selection of the isolation system or by the addition of dampers at the location of maximum water particle velocities. A theoretical solution developed from linear wave theory correlates very well with the experimental results. Further study is carried out to investigate the advantages of using base isolation for large storage tanks.
TL;DR: In this article, a new stochastic fields simulation technique that can realize prescribed means and covariances with a substantially smaller sample size than that of other existing methods is developed, utilizing the modal decomposition of the covariance matrix of the correlated random vector and the spectral representation of random processes.
Abstract: A new stochastic fields simulation technique that can realize prescribed means and covariances with a substantially smaller sample size than that of other existing methods is developed. The method utilizes the modal decomposition of the covariance matrix of the correlated random vector and the spectral representation of random processes. The decreasing feature of the eigenvalues of the covariance matrix and the orthogonality of the trigonometric functions are taken advantage of for generating sets of independent random variables. The generated discretized stochastic field is Gaussian by virtue of the central limit theorem. The sample functions of the discretized stochastic field precisely reproduces, when ensemble-averaged, the prescribed zero-mean and covariance function. Hence, the proposed statistical preconditioning technique will, in general, dramatically reduce the large computational effort that Monte Carlo simulation involving stochastic fields would otherwise entail.
TL;DR: In this paper, a damage model for monotonic and cyclic behavior of concrete is developed, which recognizes the tortuous nature of cracks in compression, which affects the flexibility of the material in a direction coinciding with the average plane of cracks.
Abstract: A damage model for monotonic and cyclic behavior of concrete is developed. The model recognizes the tortuous nature of cracks in compression, which affects the flexibility of the material in a direction coinciding with the average plane of the cracks. An elastic potential is introduced in terms of the principal stresses and a compliance tensor dependent on the accumulated damage. Damage evolution is obtained using a loading surface and bounding surface, defined in terms of the thermodynamic force conjugates of the damage variables. The damage growth during a series of unaxial compression and cyclic tests is inferred from the amplitude attenuation of ultrasonic waveforms transmitted laterally through the specimen while the tests are in progress. The behavior of concrete under compression, tension, biaxial loading and cycling, and damage growth under both monotonic and cyclic loading are found to be predicted well by the proposed theory.
TL;DR: In this article, a two-part analytic model is developed to assist in seismic response analysis of highway bridges that have abutments supported on earth embankments, which can be incorporated into a detailed dynamic model of the superstructure as the equivalent stiffnesses of a monolithic abutment system.
Abstract: A two-part analytic model is developed to assist in seismic response analysis of highway bridges that have abutments supported on earth embankments. In the first part of the model, an expression is developed for identification of the fundamental transverse frequency of the earth embankment. In the second part, two simple equivalent springs are used to represent the transverse and vertical stiffness of a monolithic abutment system. The springs are based on linear elastic plane-strain analysis of a typical trapezoidal-shaped embankment cross section. The spring stiffnesses are related to the cross-sectional dimensions and the soil properties of the earth embankment, which supports the bridge abutments. These stiffnesses can be incorporated into a detailed dynamic model of the superstructure as the equivalent stiffnesses of the bridge abutments. The frequency and the translational stiffnesses predicted by the model are in good agreement with results from a more complicated analytic theory and from finite element analysis of the abutment soil system. A companion paper illustrates an application of the model and provides comparisons to recorded earthquake responses.
TL;DR: In this paper, it was shown that the antiplane vibrations of long structures can be described by the translation of the foundation only if η (ratio of the length of structure to the wavelength of incident waves) is less than ∼ 1/1,000.
Abstract: Qualitative analysis of the antiplane vibrations of long structures shows that the dynamic response to excitation by ground waves can be described by the translation of the foundation only if η (ratio of the length of structure to the wavelength of incident waves) is less than ∼1/1,000. For 1/1,000 1/100-1/10 actual wave motion of the ground must be considered, not only for the correct representation of the dynamic response of structures, but also for proper analysis of the resulting deformation of the foundations.
TL;DR: In this article, the response of buildings with a soft first floor and excited by propagating wave motion at the base is studied, so that the physical phenomena associated with phased input excitation can be characterized.
Abstract: Simplified response of buildings with a soft first floor and excited by propagating wave motion at the base are studied, so that the physical phenomena associated with phased input excitation can be characterized. Analytical solutions are obtained for two‐dimensional continuous building models, neglecting the soil‐structure interaction, and for monochromatic antiplane excitation. It is shown that the wave energy does not always propagate from the ground into the building, depending on the value of the horizontal phase velocity of the ground motion. There is a possibility that it propagates only into the “soft” first floor, which then acts as an “isolation layer” for the upper floors. However, this is at the expense of very large deformations of the columns of the first floor, that are not considered in the conventional analysis of buildings. Also, the out‐of‐phase motion of the base may excite torsional vibrations with large amplitudes. It is concluded that the design for P‐delta effects in the soft first...
TL;DR: In this paper, a hybrid boundary element formulation method was presented to evaluate the impedance and compliance functions of piles and inclined pile groups embedded in a homogeneous soil media, and the results showed that the method is suitable for a variety of applications.
Abstract: In this paper a hybrid boundary element formulation method I is presented to evaluate the impedance and compliance functions of piles and inclined pile groups embedded in a homogeneous soil media. ...
TL;DR: In this paper, a general and efficient method for reliability and sensitivity analysis is presented for the analysis of components and systems in design situations where uncertainties are represented by a vector of random variables and a stationary Gaussian vector process.
Abstract: A general and efficient method for reliability and sensitivity analysis is presented. The methods are for the analysis of components and systems in design situations where uncertainties are represented by a vector of random variables and a stationary Gaussian vector process. A formulation as a first-passage problem for a vector process outcrossing a safe set is first applied for a fixed value of the random variable vector. This gives a conditional failure probability, and a fast integration technique based on a first- or second-order reliability method is then applied to compute the unconditional failure probability. Extensive use of analytical gradient information is made in the iteration algorithms and in the calculation of sensitivity factors. A nested first-order reliability method is proposed together with a method based on an integrated optimization for the two first-order reliability analyses. For a preliminary analysis, a “crude” first-order reliability method is described. The computation time is only a few times the computation time for a first-order reliability analysis of a similar time-independent problem. Software developed from existing special software for first-order reliability analysis or existing general optimization software can be applied.
TL;DR: In this paper, consistent tangent moduli for the generalized Duvaut-Lions viscoplasticity model are derived based on consistent linearization of the residual functions associated with two alternative unconditionally stable constitutive integration algorithms; namely, the implicit backward Euler and the full integration.
Abstract: Consistent (algorithmic) tangent moduli for the generalized Duvaut-Lions viscoplasticity model are derived in this work. The derivations are based on consistent linearization of the residual functions associated with two alternative unconditionally stable constitutive integration algorithms; namely, the implicit backward Euler and the “full integration” algorithms. This “consistent linearization” procedure is equally applicable to the Perzyna-type viscoplasticity formulations. In particular, the von Mises isotropic/kinematic hardening viscoplasticity model is chosen as a model problem for demonstration. Consistent viscoplastic tangent moduli for other choices of (single or multiple) loading surfaces can be derived in a similar fashion provided that consistent elastoplastic (inviscid) tangent moduli are available. It is noted that since continuum tangent moduli do not exist at all for viscoplasticity, use of the proposed consistent tangent modul is not only desirable but necessary in the Newton-type finite-element computations. In addition, due to the difference in the two constitutive integration algorithms used, the corresponding consistent tangent moduli are not the same even when time steps are small. Numerical examples are also presented to illustrate the remarkable quadratic performance of the proposed consistent tangent moduli for the generalized Duvaut-Lions viscoplasticity model.
TL;DR: The pseudodynamic test method is a hybrid, computer-controlled, experimental technique that adopts a step-by-step integration procedure to analyze the seismic behavior of structures as mentioned in this paper.
Abstract: The pseudodynamic test method is a hybrid, computer‐controlled, experimental technique that adopts a step‐by‐step integration procedure to analyze the seismic behavior of structures. Since the response of the structural specimen in each step of a test is evaluated with the experimental data obtained in the previous step or steps, experimental errors introduced in each step are accumulated in the numerical procedure. The error‐propagation characteristics of several integration algorithms that are currently used for such tests are examined. Mathematical equations that characterize the cumulative growth of experimental errors are formulated, and used to evaluate the error‐amplification effects of the algorithms. It is shown that the magnitude of cumulative errors depends on the numerical properties of the algorithm, the frequency characteristics of the specimen, and the nature of experimental errors. Moreover, it is found that numerically computed displacements should be used instead of experimentally measur...
TL;DR: In this paper, the applicability of the uniform strain assumption is evaluated by comparing the results from the micro-structural continuum method to those from the computer simulation method, and two types of granular solids, viz. with linear bonded contacts and with nonlinear frictional contacts, are studied to investigate the influence of contact behavior on the heterogeneity of the strain field.
Abstract: The micro‐ and the macro‐mechanical measures of heterogeneous granular solids are investigated using two methods, namely a computer simulation method, and a micro‐structural continuum method. The micro‐structural continuum method used in this study is based on a uniform strain assumption. The applicability of the uniform strain assumption is evaluated by comparing the results from the micro‐structural continuum method to those from the computer simulation method. Two types of granular solids, viz. with linear bonded contacts and with nonlinear frictional contacts, are studied to investigate the influence of contact behavior on the heterogeneity of the strain field. It is observed that packings with bonded contacts have a reasonably homogeneous strain field, implying that the uniform strain assumption is applicable for this condition. Packings with frictional contacts have a heterogeneous strain field, except at low levels of deviatoric stress. The natures of inhomogeneity for the particle rotation, stress...
TL;DR: In this paper, a real-time, time-domain system-identification technique is developed to identify time-varying system parameters for a multidegree-of-freedom degrading structure subjected to general dynamic loads, such as earthquakes.
Abstract: On-line identification becomes an important issue when structures undergo nonlinear and time-dependent degrading behavior under large loads. In this paper, a real-time, time-domain system-identification technique is developed to identify time-varying system parameters for a multidegree-of-freedom degrading structure subjected to general dynamic loads, such as earthquakes. A system of second-order, linear, ordinary differential equations with time-varying system parameters is solved to generate the system response using the Newmark time-integration method. Gaussian white noise is added to the response and the results are used to simulate the measurements. Then, a least-square’s method is employed to estimate the system parameters in real time based on input data and corresponding response measurements with or without noise. Two numerical examples, a single-degree-of-freedom and a three-degree-of-freedom structure subjected to a simulated El Centro earthquake, are considered. The changes in structural stiffnesses for the example problems are identified. Encouraging results are obtained for both cases.
TL;DR: In this article, a continuum theory is presented for representing the high-temperature deformation behavior of metallic composite materials, where the composite is considered pseudohomogeneous with its own properties that can be measured for the composite as a whole.
Abstract: A continuum theory is presented for representing the high‐temperature deformation behavior of metallic composite materials. The composite is considered pseudohomogeneous with its own properties that can be measured for the composite as a whole. A class of constitutive equations in which the inelastic strain rate and internal state are expressible as gradients of a dissipation potential function is extended for a composite. The potential is taken to depend on invariants that reflect local transverse isotropy. Applications illustrate the capability of the theory of representing the time‐dependent, hereditary, anisotropic behavior typical of these materials at elevated temperature.
TL;DR: In this article, an approximate deterministic method of analysis is presented for assessing the effects of ground-motion incoherence and of the associated soil-structure interaction on the seismic response of structure-foundation-soil systems.
Abstract: An approximate deterministic method of analysis is presented for assessing the effects of ground‐motion incoherence and of the associated soil‐structure interaction on the seismic response of structure‐foundation‐soil systems. The free‐field ground motion in this approach is specified by an acceleration history and a spatial incoherence function. Numerical solutions are presented that illustrate the procedure and elucidate the nature and relative importance of the kinematic and inertial interaction effects. The results are shown to be consistent with those obtained in a recent companion study by formal application of the stochastic approach.
TL;DR: In this article, a particle velocity distribution function is first obtained in the equilibrium state or in dilute steady state for the particle in two-phase flows, then a theoretical model for particle concentration distribution is derived from the kinetic theory.
Abstract: The results of experiments in open channels and closed pipelines show two kinds of patterns for the vertical distribution of particle concentration (ie, pattern I and pattern II) The former shows a pattern of maximum concentration at some location above the bottom and the downward decay of the concentration below the location The latter always shows an increase of the particle concentration downward over the whole vertical, with the maximum value at the bottom Many investigations were made on the pattern II, but few were made on pattern I In this paper, a particle velocity distribution function is first obtained in the equilibrium state or in dilute steady state for the particle in two-phase flows, then a theoretical model for the particle concentration distribution is derived from the kinetic theory More attention is paid to the predictions of the concentration distribution of pattern I and comparisons of the present model are made with the data measured by means of laser doppler anemometry (LDA) Very good agreements are obtained between the measured and calculated results
TL;DR: In this article, the probabilistic finite element method (PFEM) was extended to probabilistically fracture mechanics (PFM) using an enriched element that has the near crack-tip singular strain field embedded.
Abstract: The fusion of the probabilistic finite element method (PFEM) and reliability analysis for probabilistic fracture mechanics (PFM) is presented. The PFEM is extended to PFM using an enriched element that has the near crack‐tip singular strain field embedded. Static condensation is used to solve for modes I and II stress intensity factors, and the adjoint approach to PFEM is employed for evaluating the derivatives of the stress intensity factors with respect to the random variables. Statistical moments (e.g., expectation, covariance, and correlation) of stress intensity factors are calculated for uncertainties in load, material properties including fracture toughness, component geometry, and crack geometry (i.e., crack length, orientation, and position). In addition, the first‐order probability of brittle fracture is calculated. In order to calculate the probability of fracture, an optimization procedure is employed to determine the reliability index. The methodology is demonstrated on two mode I fracture ex...